5 papers
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…