{"id":41119,"date":"2024-09-26T06:30:32","date_gmt":"2024-09-26T06:30:32","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7%db%8c%db%8c-%d8%a8%d8%a7-%d9%be%db%8c%d9%88%d9%86%d8%af\/"},"modified":"2024-09-26T06:30:33","modified_gmt":"2024-09-26T06:30:33","slug":"%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7%db%8c%db%8c-%d8%a8%d8%a7-%d9%be%db%8c%d9%88%d9%86%d8%af","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d8%aa%d8%b1%d8%ac%d9%85%d9%87-%d9%81%d8%a7%d8%b1%d8%b3%db%8c-%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%86%d9%85%d9%88%d8%af%d8%a7%d8%b1%d9%87%d8%a7%db%8c%db%8c-%d8%a8%d8%a7-%d9%be%db%8c%d9%88%d9%86%d8%af\/","title":{"rendered":"\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc\u06cc \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f\u0647\u0627\u06cc \u062b\u0627\u0628\u062a \u0648 \u0634\u0645\u0627\u0631\u0647 \u0647\u0627\u06cc Tur\u00e1n \u0627\u0644\u0642\u0627 \u0634\u062f\u0647"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nGraphs with constant links and induced Tur\u00e1n numbers<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc\u06cc \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f\u0647\u0627\u06cc \u062b\u0627\u0628\u062a \u0648 \u0634\u0645\u0627\u0631\u0647 \u0647\u0627\u06cc Tur\u00e1n \u0627\u0644\u0642\u0627 \u0634\u062f\u0647<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nYair Caro, Adriana Hansberg, Zsolt Tuza<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nPDF<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u062a\u062d\u0648\u06cc\u0644\u06cc <\/td>\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647 \u062a\u0631\u062c\u0645\u0647 \u0634\u062f\u0647 <\/td>\n\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\n<\/tr>\n
\u0646\u062d\u0648\u0647 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 <\/td>\n\u062f\u0648 \u062a\u0627 \u0633\u0647 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634 (\u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u062f\u0627\u0646\u0644\u0648\u062f\u06cc)<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n23<\/td>\n<\/tr>\n
\u0644\u06cc\u0646\u06a9 \u062f\u0627\u0646\u0644\u0648\u062f \u0631\u0627\u06cc\u06af\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n\u062f\u0627\u0646\u0644\u0648\u062f \u0645\u0642\u0627\u0644\u0647<\/a><\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nCombinatorics,\u062a\u0631\u06a9\u06cc\u0628\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 19 September, 2024; originally announced September 2024. , Comments: 23 pages, 5 figures , MSC Class: 05B05; 05B25; 05C35; 05C65<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 \u062f\u0631 19 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u0633\u067e\u062a\u0627\u0645\u0628\u0631 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 23 \u0635\u0641\u062d\u0647 \u060c 5 \u0634\u06a9\u0644 \u060c \u06a9\u0644\u0627\u0633 MSC: 05B05 \u061b05B25 \u061b05C35 \u061b05C65<\/td>\n<\/tr>\n
\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u0627\u0632 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u067e\u0627\u06cc\u06af\u0627\u0647 \u0647\u0627\u06cc \u0639\u0644\u0645\u06cc <\/td>\n\n INSPIRE HEP<\/a>
\n
\n NASA ADS<\/a>
\n
\n Google Scholar<\/a>
\n
\n Semantic Scholar<\/a>
\n
\n arXiv<\/a><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\r\n\r\n \r\n \r\n \r\n \r\n
\u0641\u0631\u0645\u062a \u0627\u0631\u0627\u0626\u0647 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u062a\u062d\u0648\u06cc\u0644 \u0628\u0647 \u0635\u0648\u0631\u062a \u0641\u0627\u06cc\u0644 \u0648\u0631\u062f<\/td>\r\n <\/tr>\r\n
\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 <\/td>\r\n \u0628\u06cc\u0646 2 \u062a\u0627 3 \u0631\u0648\u0632 \u067e\u0633 \u0627\u0632 \u062b\u0628\u062a \u0633\u0641\u0627\u0631\u0634<\/td>\r\n <\/tr>\r\n\t
\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 <\/td>\r\n \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.<\/td>\r\n <\/tr>\r\n\t\t
\u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 <\/td>\r\n \u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.<\/td>\r\n <\/tr>\r\n<\/table>\r\n\r\n\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

A graph $G$ of constant link $L$ is a graph in which the neighborhood of any vertex induces a graph isomorphic to $L$. Given two different graphs, $H$ and $G$, the induced Tur\u00e1n number ${\\rm ex}(n; H, G{\\rm -ind})$ is defined as the maximum number of edges in an $n$-vertex graph having no subgraph isomorphic to $H$ and no copy from $G$ as an induced subgraph. Our main motivation in this paper is to establish a bridge between graphs with constant link and induced Tur\u00e1n numbers via the class of $t$-regular, $k$-uniform (linear) hypergraphs of girth at least $4$, as well as to present several methods of constructing connected graphs with constant link. We show that, for integers $t \\geq 3$ and $k \\geq 3$, ${\\rm ex}(n; C_k, K_{1,t}{\\rm -ind}) \\leq (k – 2)(t – 1)n\/2$ and that equality holds for infinitely many values of $n$. This result is built upon the existence of graphs with constant link $tL$ with restricted cycle length, which we prove in another theorem. More precisely, we show that, given a graph $F$ with constant link $L$ and circumference $c$, then, for all integers $t \\geq 2$ and $g > c$, there exists a graph with constant link $tL$ which is free of cycles of length $l$, for all $c < l < g$. We provide two proofs of this result using distinct approaches. We further present constructions of graphs with constant links $tL$, $t \\geq 2$, and restricted cycle length based on Steiner Systems. Finally, starting from a connected graph of constant link $tL$, for $t \\geq 2$, having order $n$ and restricted cycle lengths, we provide a method to construct an infinite collection of connected graphs of constant link $tL$ that preserves the cycle length restriction, and whose orders form an arithmetic progression $qn$, $q \\geq 1$.<\/p>\n

\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n

\u0646\u0645\u0648\u062f\u0627\u0631 $ g $ \u067e\u06cc\u0648\u0646\u062f \u062b\u0627\u0628\u062a $ L $ \u0646\u0645\u0627\u062f\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0646 \u0645\u062d\u0644\u0647 \u0647\u0631 \u0631\u0627\u0633 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0646\u0645\u0648\u062f\u0627\u0631 \u0631\u0627 \u0628\u0647 $ L $ \u0627\u0644\u0642\u0627 \u0645\u06cc \u06a9\u0646\u062f.\u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u062f\u0648 \u0646\u0645\u0648\u062f\u0627\u0631 \u0645\u062e\u062a\u0644\u0641 \u060c $ H $ \u0648 $ g $ \u060c \u0634\u0645\u0627\u0631\u0647 Tur\u00e1n \u0627\u0644\u0642\u0627 \u0634\u062f\u0647 $ {\\ rm ex} (n \u061b h \u060c g {\\ rm -ind}) $ \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u062d\u062f\u0627\u06a9\u062b\u0631 \u062a\u0639\u062f\u0627\u062f \u0644\u0628\u0647 \u0647\u0627 \u062f\u0631 $ n $ \u062a\u0639\u0631\u06cc\u0641 \u0634\u062f\u0647 \u0627\u0633\u062a-\u0646\u0645\u0648\u062f\u0627\u0631 Vertex \u06a9\u0647 \u062f\u0627\u0631\u0627\u06cc \u0632\u06cc\u0631\u06af\u0631\u0627\u0641 \u0627\u06cc\u0632\u0648\u0645\u0648\u0631\u0641\u06cc\u06a9 \u062a\u0627 $ H $ \u0648 \u0628\u062f\u0648\u0646 \u0646\u0633\u062e\u0647 \u0627\u0632 $ g $ \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0632\u06cc\u0631\u06af\u0631\u0627\u0641 \u0627\u0644\u0642\u0627 \u0634\u062f\u0647 \u0627\u0633\u062a.\u0627\u0646\u06af\u06cc\u0632\u0647 \u0627\u0635\u0644\u06cc \u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0627\u06cc\u062c\u0627\u062f \u067e\u0644\u06cc \u0628\u06cc\u0646 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f \u062b\u0627\u0628\u062a \u0648 \u0627\u0639\u062f\u0627\u062f Tur\u00e1n \u0627\u0644\u0642\u0627 \u0634\u062f\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u06a9\u0644\u0627\u0633 $ t $ -regular \u060c $ k $ -inuform (\u062e\u0637\u06cc) Hypergraphs \u062d\u062f\u0627\u0642\u0644 4 $ $ \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0647\u0686\u0646\u062f\u06cc\u0646 \u0631\u0648\u0634 \u0628\u0631\u0627\u06cc \u0633\u0627\u062e\u062a \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u0645\u062a\u0635\u0644 \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f \u062b\u0627\u0628\u062a \u0627\u0631\u0627\u0626\u0647 \u062f\u0647\u06cc\u062f.\u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u060c \u0628\u0631\u0627\u06cc \u0639\u062f\u062f \u0635\u062d\u06cc\u062d $ t \\ geq 3 $ \u0648 $ k \\ geq 3 $ \u060c $ {\\ rm ex} (n \u061b c_k \u060c k_ {1 \u060c t} {\\ rm -ind}) \\ leq (k – 2) (t – 1) n\/2 $ \u0648 \u0622\u0646 \u0628\u0631\u0627\u0628\u0631\u06cc \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u062f\u06cc\u0631 \u0628\u06cc \u0646\u0647\u0627\u06cc\u062a \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 $ n $ \u0631\u0627 \u062f\u0631 \u062e\u0648\u062f \u062c\u0627\u06cc \u062f\u0627\u062f\u0647 \u0627\u0633\u062a.\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0648\u062c\u0648\u062f \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f \u062b\u0627\u0628\u062a $ tl $ \u0628\u0627 \u0637\u0648\u0644 \u0686\u0631\u062e\u0647 \u0645\u062d\u062f\u0648\u062f \u0633\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0627\u0633\u062a \u060c \u06a9\u0647 \u0645\u0627 \u062f\u0631 \u06cc\u06a9 \u0642\u0636\u06cc\u0647 \u062f\u06cc\u06af\u0631 \u0627\u062b\u0628\u0627\u062a \u0645\u06cc \u06a9\u0646\u06cc\u0645.\u0628\u0647 \u0637\u0648\u0631 \u062f\u0642\u06cc\u0642 \u062a\u0631 \u060c \u0645\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0627 \u062a\u0648\u062c\u0647 \u0628\u0647 \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 $ f $ \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f \u062b\u0627\u0628\u062a $ l $ \u0648 \u062f\u0648\u0631 $ c $ \u060c \u0633\u067e\u0633 \u060c \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0639\u062f\u062f \u0635\u062d\u06cc\u062d $ t \\ geq 2 $ \u0648 $ g> c $ \u060c \u06cc\u06a9 \u0646\u0645\u0648\u062f\u0627\u0631 \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f \u062b\u0627\u0628\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f$ tl $ \u06a9\u0647 \u0639\u0627\u0631\u06cc \u0627\u0632 \u0686\u0631\u062e\u0647 \u0637\u0648\u0644 $ L $ \u0627\u0633\u062a \u060c \u0628\u0631\u0627\u06cc \u062a\u0645\u0627\u0645 $ c \n","protected":false},"excerpt":{"rendered":"

\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Graphs with constant links and induced Tur\u00e1n numbers \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc\u06cc […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"open","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[21],"product_tag":[],"class_list":{"0":"post-41119","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-21","7":"pmpro-has-access","8":"desktop-align-left","9":"tablet-align-left","10":"mobile-align-left","12":"first","13":"instock","14":"downloadable","15":"shipping-taxable","16":"purchasable","17":"product-type-simple"},"yoast_head":"\n\u062a\u0631\u062c\u0645\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc\u06cc \u0628\u0627 \u067e\u06cc\u0648\u0646\u062f\u0647\u0627\u06cc \u062b\u0627\u0628\u062a \u0648 \u0634\u0645\u0627\u0631\u0647 \u0647\u0627\u06cc Tur\u00e1n \u0627\u0644\u0642\u0627 \u0634\u062f\u0647 - 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