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pro vyhledávání: '"Miao, Zhengke"'
For any positive integer $k$, the reconfiguration graph for all $k$-colorings of a graph $G$, denoted by $\mathcal{R}_k(G)$, is the graph where vertices represent the $k$-colorings of $G$, and two $k$-colorings are joined by an edge if they differ in
Externí odkaz:
http://arxiv.org/abs/2409.19368
Bermond, Jackson and Jaeger [{\em J. Combin. Theory Ser. B} 35 (1983): 297-308] proved that every bridgeless ordinary graph $G$ has a circuit $4$-cover and Fan [{\em J. Combin. Theory Ser. B} 54 (1992): 113-122] showed that $G$ has a circuit $6$-cove
Externí odkaz:
http://arxiv.org/abs/2310.17098
In this paper we investigate Ramanujan hypergraphs by using hypergraph coverings. We first show that the spectrum of a $k$-fold covering $\bar{H}$ of a connected hypergraph $H$ contains the spectrum of $H$, and that it is the union of the spectrum of
Externí odkaz:
http://arxiv.org/abs/2310.01771
In this paper, by developing several new adjacency lemmas about a path on $4$ or $5$ vertices, we show that the average degree of 7-critical graphs is at least 6. It implies Vizing's planar graph conjecture for planar graphs with maximum degree $7$ a
Externí odkaz:
http://arxiv.org/abs/2301.02140
A well-known theorem of Vizing states that if $G$ is a simple graph with maximum degree $\Delta$, then the chromatic index $\chi'(G)$ of $G$ is $\Delta$ or $\Delta+1$. A graph $G$ is class 1 if $\chi'(G)=\Delta$, and class 2 if $\chi'(G)=\Delta+1$; $
Externí odkaz:
http://arxiv.org/abs/2109.00466
A star $k$-edge coloring is a proper edge coloring such that there are no bichromatic paths or cycles of length four. The smallest integer $k$ such that $G$ admits a star $k$-edge coloring is the star chromatic index of $G$. Deng \etal \cite{MR293383
Externí odkaz:
http://arxiv.org/abs/2104.05958
Publikováno v:
In Discrete Mathematics January 2024 347(1)
Publikováno v:
In Discrete Applied Mathematics 15 April 2023 329:96-105
Publikováno v:
In Discrete Mathematics January 2023 346(1)
Publikováno v:
In Journal of Combinatorial Theory, Series B March 2022 153:61-80