Near-perfect clique-factors in sparse pseudorandom graphs

Q2 Mathematics
Jie Han , Yoshiharu Kohayakawa , Yury Person
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引用次数: 7

Abstract

We prove that, for any t3, there exists a constant c=c(t)>0 such that any d-regular n-vertex graph with the second largest eigenvalue in absolute value λ satisfying λcdt1/nt2 contains (1o(1))n/t vertex-disjoint copies of Kt. This provides further support for the conjecture of Krivelevich, Sudakov and Szábo [Triangle factors in sparse pseudo-random graphs, Combinatorica 24 (2004), pp. 403–426] that (n,d,λ)-graphs with n3N and λcd2 for a suitably small absolute constant c>0 contain triangle-factors.

稀疏伪随机图中近乎完美的派系因子
我们证明了,对于任意t≥3,存在一个常数c=c(t)>0,使得任何d-正则n顶点图,其绝对值λ满足λ≤cdt−1/nt−2,其第二大特征值包含Kt的(1−o(1))个不相交的顶点拷贝。这进一步支持了Krivelevich, Sudakov和Szábo的猜想[稀疏伪随机图中的三角形因子,Combinatorica 24 (2004), pp. 403-426],即n∈3N且λ≤cd2的(n,d,λ)-图对于一个适当小的绝对常数c>0包含三角形因子。
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来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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