1 citations · 1 across the 11 of their papers we have counts for
11 papers
An improved upper bound for the planar Turán number of
Xuqing Bai, Weichan Liu, Xiangxiang Nie +1
We prove that every -vertex simple planar graph with no copy of has at most \[ \frac{69}{25}(n-2) \] edges, for every . This improves the best known bound \[ \frac…
Bootstrap percolation of extension hypergraphs
Weichan Liu, Bjarne Schülke, Xin Zhang
For -graphs and the -bootstrap percolation process (or -process) starting with is a sequence of -graphs such that is obtained…
Between proper and square colorings of planar graphs with maximum degree at most four
Xujun Liu, Zihui Xu, Xin Zhang
An -independent set is a vertex set whose pairwise distance is at least . A proper (square) -coloring of a graph is a partition of its vertex set into independen…
On -packing edge-coloring of sparse subcubic graphs
Xujun Liu, Jiacheng Yang, Xin Zhang
For positive integers and , a -packing edge-coloring of a graph is a partition of into matchings and induced matchings. A graph is $d…
Exact rainbow numbers of cycle-related graphs in multi-hubbed wheels
Mengyao Dai, Xin Zhang
The rainbow number is the minimum number of colors for which any edge-coloring of with at least colors guarantees a rainbow subgraph isomorphic to .…
Fast algorithm for -packing coloring of Halin graphs
Xin Zhang, Dezhi Zou
Motivated by frequency assignment problems in wireless broadcast networks, Goddard, Hedetniemi, Hedetniemi, Harris, and Rall introduced the notion of -packing coloring in 2008.…
Proper conflict-free choosability of planar graphs
Yuting Wang, Xin Zhang
A proper conflict-free coloring of a graph is a proper vertex coloring wherein each non-isolated vertex's open neighborhood contains at least one color appearing exactly once. For…
Independent transversal blow-up of graphs
Tianjiao Dai, Weichan Liu, Xin Zhang
In an -partite graph, an independent transversal of size (ITS) consists of vertices from each part forming an independent set. Motivated by a question from Bollobás, Erd…
Equitable coloring of sparse graphs
Weichan Liu, Xin Zhang
An equitable coloring of a graph is a proper coloring where the sizes of any two distinct color classes differ by at most one. The celebrated Chen-Lih-Wu Conjecture (CLWC for short…
Cooperative colorings of hypergraphs
Xuqing Bai, Bi Li, Weichan Liu +1
Given a class of hypergraphs with the same vertex set , a cooperative coloring of them is a partition …
Every subcubic graph is packing -colorable
Xujun Liu, Xin Zhang, Yanting Zhang
For a sequence of non-decreasing integers, a packing -coloring of a graph is a partition of its vertex set into such that fo…