无3环或4环的平衡3部图的密度

IF 0.7 4区 数学 Q2 MATHEMATICS
Zequn Lv, Mei Lu, Chunqiu Fang
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引用次数: 1

摘要

设$C_k$为顺序的一个循环$k$,其中$k\ge 3$。设ex $(n, n, n, \{C_{3}, C_{4}\})$为平衡的$3$部图的最大边数,该图的顶点集由三个部分组成,每个部分都有$n$个顶点,并且没有同$C_3$或$C_4$同构的子图。我们构造了没有3环和4环的稠密平衡3部图,并证明了ex $(n, n, n, \{C_{3}, C_{4}\})\ge (\frac{6\sqrt{2}-8}{(\sqrt{2}-1)^{3/2}}+o(1))n^{3/2}$。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Density of Balanced 3-Partite Graphs without 3-Cycles or 4-Cycles
Let $C_k$ be a cycle of order $k$, where $k\ge 3$. Let ex$(n, n, n, \{C_{3}, C_{4}\})$ be the maximum number of edges in a balanced $3$-partite graph whose vertex set consists of three parts, each has $n$ vertices that has no subgraph isomorphic to $C_3$ or $C_4$. We construct dense balanced 3-partite graphs without 3-cycles or 4-cycles and show that ex$(n, n, n, \{C_{3}, C_{4}\})\ge (\frac{6\sqrt{2}-8}{(\sqrt{2}-1)^{3/2}}+o(1))n^{3/2}$.
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来源期刊
CiteScore
1.30
自引率
14.30%
发文量
212
审稿时长
3-6 weeks
期刊介绍: The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.
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