Yan Zhao

activity

20122026

most citedOn (strong) proper vertex-connection of graphs

2 citations · 7 across the 12 of their papers we have counts for

collaborators

13 papers

math.CO2026

Induced Ramsey numbers for fans

Chuang Zhong, Masaki Kashima, Yaping Mao +1

The induced Ramsey number $r_{ind} (G, H)$ is defined as the minimum order of a graph $F$ on such that any 2-coloring of its edges with red and blue leads to either a red in…

math.CO2020

Note on Path-Connectivity of Complete Bipartite Graphs

Shasha Li, Yan Zhao

For a graph $G = (V, E)$ and a set $S \subseteq V (G)$ of size at least $2$ , a path in $G$ is said to be an $S$ -path if it connects all vertices of $S$ . Two $S$ -paths $P_{1}$ and $P_{2}$ ar…

math.CO2017

On the complexity of k-rainbow cycle colouring problems

Shasha Li, Yongtang Shi, Jianhua Tu +1

An edge-coloured cycle is $r ainb o w$ if all edges of the cycle have distinct colours. For $k \geq 1$ , let $F_{k}$ denote the family of all graphs with the property that any…

math.CO2015★ 2 cited

On (strong) proper vertex-connection of graphs

Hui Jiang, Xueliang Li, Yingying Zhang +1

A path in a vertex-colored graph is a {\it vertex-proper path} if any two internal adjacent vertices differ in color. A vertex-colored graph is {\it proper vertex $k$ -connected} if…

math.CO2014

Note on the upper bound of the rainbow index of a graph

Qingqiong Cai, Xueliang Li, Yan Zhao

A path in an edge-colored graph $G$ , where adjacent edges may be colored the same, is a rainbow path if every two edges of it receive distinct colors. The rainbow connection number…

math.CO2014★ 1 cited

The 3-rainbow index and connected dominating sets

Qingqiong Cai, Xueliang Li, Yan Zhao

A tree in an edge-colored graph is said to be rainbow if no two edges on the tree share the same color. An edge-coloring of $G$ is called 3-rainbow if for any three vertices in $G$ …

math.CO2014

The generalized 3-edge-connectivity of lexicographic product graphs

Xueliang Li, Jun Yue, Yan Zhao

The generalized $k$ -edge-connectivity $λ_{k} (G)$ of a graph $G$ is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs $G$ and $H$ , denoted…

math.CO2013★ 1 cited

Graphs with $4$ -rainbow index $3$ and $n - 1$

Xueliang Li, Ingo Schiermeyer, Kang Yang +1

Let $G$ be a nontrivial connected graph with an edge-coloring $c : E (G) \to {1, 2, \dots, q},$ $q \in N$ , where adjacent edges may be colored the same. A tree $T$ in $…

math.CO2013

Characterize graphs with rainbow connection number $m - 2$ and $m - 3$

Xueliang Li, Yuefang Sun, Yan Zhao

A path in an edge-colored graph, where adjacent edges may be colored the same, is a rainbow path if no two edges of it are colored the same. A nontrivial connected graph $G$ is rai…

math.CO2013★ 1 cited

Graphs with 3-rainbow index $n - 1$ and $n - 2$

Xueliang Li, Kang Yang, Yan Zhao

Let $G$ be a nontrivial connected graph with an edge-coloring $c : E (G) \to {1, 2, \dots, q},$ $q \in N$ , where adjacent edges may be colored the same. A tree $T$ in $…

math.CO2013

The 3-rainbow index of a graph

Lily Chen, Xueliang Li, Kang Yang +1

Let $G$ be a nontrivial connected graph with an edge-coloring $c : E (G) \to {1, 2, ..., q},$ $q \in N$ , where adjacent edges may be colored the same. A tree $T$ in $G…

math.CO2013★ 2 cited

On extremal graphs with exactly one Steiner tree connecting any $k$ vertices

Xueliang Li, Yan Zhao

The problem of determining the largest number $f (n; κ ˉ \leq ℓ)$ of edges for graphs with $n$ vertices and maximal local connectivity at most $ℓ$ was considered by Bollobás.…

math.CO2012

Note on minimally $k$ -rainbow connected graphs

Hengzhe Li, Xueliang Li, Yuefang Sun +1

An edge-colored graph $G$ , where adjacent edges may have the same color, is {\it rainbow connected} if every two vertices of $G$ are connected by a path whose edge has distinct col…