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of 652
pro vyhledávání: '"Lai, Hong‐Jian"'
In 1967, Katona and Szemer\'{e}di showed that no undirected graph with $n$ vertices and fewer than $\frac{n}{2}\log_2\frac{n}{2}$ edges admits an orientation of diameter two. In 1978, Chv\'atal and Thomassen revealed the complexity of determining whe
Externí odkaz:
http://arxiv.org/abs/2408.10809
The \textit{square} of a graph $G$, denoted by $G^2$, is obtained from $G$ by adding an edge to connect every pair of vertices with a common neighbor in $G$. In this paper we prove that for every planar graph $G$ with maximum degree at most $5$, $G^2
Externí odkaz:
http://arxiv.org/abs/2308.01824
A mixed graph $\widetilde{G}$ is obtained from a simple undirected graph $G$, the underlying graph of $\widetilde{G}$, by orienting some edges of $G$. Let $c(G)=|E(G)|-|V(G)|+\omega(G)$ be the cyclomatic number of $G$ with $\omega(G)$ the number of c
Externí odkaz:
http://arxiv.org/abs/2304.06239
Publikováno v:
In Discrete Applied Mathematics 15 August 2024 353:4-11
Publikováno v:
In Discrete Applied Mathematics 15 December 2024 358:176-183
Given two non-empty graphs $G,H$ and a positive integer $k$, the Gallai-Ramsey number $\operatorname{gr}_k(G:H)$ is defined as the minimum integer $N$ such that for all $n\geq N$, every $k$-edge-coloring of $K_n$ contains either a rainbow colored cop
Externí odkaz:
http://arxiv.org/abs/2109.13678
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 24, no. 1, Graph Theory (June 13, 2022) dmtcs:8484
For a non-negative integer $s\le |V(G)|-3$, a graph $G$ is $s$-Hamiltonian if the removal of any $k\le s$ vertices results in a Hamiltonian graph. Given a connected simple graph $G$ that is not isomorphic to a path, a cycle, or a $K_{1,3}$, let $\del
Externí odkaz:
http://arxiv.org/abs/2109.05660
Publikováno v:
In Discrete Mathematics April 2024 347(4)
A fractional matching of a graph $G$ is a function $f:E(G) \to [0,1]$ such that for any $v\in V(G)$, $\sum_{e\in E_G(v)}f(e)\leq 1$ where $E_G(v) = \{e \in E(G): e$ is incident with $v$ in $G\}$. The fractional matching number of $G$ is $\mu_{f}(G) =
Externí odkaz:
http://arxiv.org/abs/2002.00370
Let $\kappa'(G)$, $\kappa(G)$, $\mu_{n-1}(G)$ and $\mu_1(G)$ denote the edge-connectivity, vertex-connectivity, the algebraic connectivity and the Laplacian spectral radius of $G$, respectively. In this paper, we prove that for integers $k\geq 2$ and
Externí odkaz:
http://arxiv.org/abs/2001.00740