Zobrazeno 1 - 10
of 196
pro vyhledávání: '"Hou, Xinmin"'
Autor:
Sun, Jin, Hou, Xinmin
Ramsey's Theorem states that a graph $G$ has bounded order if and only if $G$ contains no complete graph $K_n$ or empty graph $E_n$ as its induced subgraph. The Gy\'arf\'as-Sumner conjecture says that a graph $G$ has bounded chromatic number if and o
Externí odkaz:
http://arxiv.org/abs/2406.01890
Let $\delta^{0}(D)$ be the minimum semi-degree of an oriented graph $D$. Jackson (1981) proved that every oriented graph $D$ with $\delta^{0}(D)\geq k$ contains a directed path of length $2k$ when $|V(D)|>2k+2$, and a directed Hamilton cycle when $|V
Externí odkaz:
http://arxiv.org/abs/2401.05205
A digraph $D$ is $k$-linked if for any pair of two disjoint sets $\{x_{1},x_{2},\ldots,x_{k}\}$ and $\{y_{1},y_{2},\ldots,y_{k}\}$ of vertices in $D$, there exist vertex disjoint dipaths $P_{1},P_{2},\ldots,P_{k}$ such that $P_{i}$ is a dipath from $
Externí odkaz:
http://arxiv.org/abs/2311.04068
In this paper, we investigate the minimum number of triangles, denoted by $t(n,k)$, in $n$-vertex $k$-regular graphs, where $n$ is an odd integer and $k$ is an even integer. The well-known Andr\'asfai-Erd\H{o}s-S\'os Theorem has established that $t(n
Externí odkaz:
http://arxiv.org/abs/2309.02993
Autor:
Jiang, Taiping, Hou, Xinmin
Given two graphs $G$ and $H$, the {Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that every 2-coloring of the edges of $K_{N}$ contains either a red $G$ or a blue $H$. Let $K_{N-1}\sqcup K_{1,k}$ be the graph obtained from $K_{N-1
Externí odkaz:
http://arxiv.org/abs/2308.10546
Given two $r$-uniform hypergraphs $F$ and $H$, we say that $H$ has an $F$-covering if every vertex in $H$ is contained in a copy of $F$. Let $c_{i}(n,F)$ be the least integer such that every $n$-vertex $r$-graph $H$ with $\delta_{i}(H)>c_i(n,F)$ has
Externí odkaz:
http://arxiv.org/abs/2308.10059
Autor:
Zhang, Xuejun, Hou, Xinmin
For given simple graphs $H_1,H_2,\dots,H_c$, the multicolor Ramsey number $R(H_1,H_2,\dots,H_c)$ is defined as the smallest positive integer $n$ such that for an arbitrary edge-decomposition $\{G_i\}^c_{i=1}$ of the complete graph $K_n$, at least one
Externí odkaz:
http://arxiv.org/abs/2308.09950
Autor:
Sun, Jin, Hou, Xinmin
The following inequality chain $$ ir(G)\le \gamma(G)\le i(G)\le \alpha(G) \le \Gamma(G) \le I\!R(G)$$ is known as a domination chain, where $ir(G), \gamma(G), i(G), \alpha(G), \Gamma(G)$, and $I\!R(G)$ are the lower irredundance number, the dominatio
Externí odkaz:
http://arxiv.org/abs/2308.07667
Autor:
Ma, Yue, Hou, Xinmin
Let $\mathcal{G}_n^k=\{G_1,G_2,\ldots,G_k\}$ be a multiset of graphs on vertex set $[n]$ and let $F$ be a fixed graph with edge set $F=\{e_1, e_2,\ldots, e_m\}$ and $k\ge m$. We say ${\mathcal{G}_n^k}$ is rainbow $F$-free if there is no $\{i_1, i_2,\
Externí odkaz:
http://arxiv.org/abs/2306.12222
Autor:
Zeng, Jiasheng, Hou, Xinmin
Chung, F\"uredi, Graham, and Seymour (JCTA, 1988) constructed an induced subgraph of the hypercube $Q^n$ with $\alpha(Q^n)+1$ vertices and with maximum degree smaller than $\lceil \sqrt{n} \rceil$. Subsequently, Huang (Annals of Mathematics, 2019) pr
Externí odkaz:
http://arxiv.org/abs/2306.04110