3 papers
math.CO2025
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 Erdős-Rényi random graph with above the connectivity threshold, t…
math.CO2025
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…
math.CO2024
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…