3 papers
math.CO2026
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.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 ErdÅs-Rényi random graph with above the connectivity threshold,…
math.CO2025
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…