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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
Colour-biased Hamilton cycles in randomly perturbed graphs
Wenchong Chen, Xinbu Cheng, Zhifei Yan
Given a graph and an -edge-colouring on , a Hamilton cycle is said to have colour-bias if contains edges of the same colour in . Fr…
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…