6 papers
Linear Lower Bounds for the Modular Chromatic Index
Xiao-Chuan Liu, Boyan Xu, Xu Yang
Let be an integer. A edge-coloring of a graph is an edge-coloring in which every nonzero degree in each color class is congruent to modulo . Let $Ï'…
Large Monochromatic Components in Colored Random Graphs
Xiao-Chuan Liu, Xu Yang
We study the size of the largest monochromatic connected component that must appear in any edge-coloring of a random graph. Let with and , and wri…
On Turán Number of Graphs with Small Minimum Feedback Vertex Numbers
Xiao-Chuan Liu, Xu Yang
Given a graph , the minimum feedback vertex number of is the minimum number of vertices whose removal results in an acyclic graph. In this paper, we investigate Turán-type…
A Note on Weak Saturation Number of Trees
Wenchong Chen, Xiao-Chuan Liu, Xu Yang
In this paper, we estimate the weak saturation numbers of trees. As a case study, we examine caterpillars and obtain several tight estimates. In particular, this implies that for a…
On the Color Discrepancy of Spanning Trees in Random and Randomly Perturbed Graphs
Wenchong Chen, Xiao-Chuan Liu, Xu Yang
In this work, we study the color discrepancy of spanning trees in random graphs. We show that for the ErdÅs-Rényi random graph with above the connectivity threshold,…
On Graph Odd Edge-Colorings and Odd Edge-Coverings
Xiao-Chuan Liu, Mirko Petruševski, Xu Yang
An odd -edge-coloring of a graph is a (not necessarily proper) edge-coloring with at most colors such that each non-empty color class induces a graph in which every vert…