7 papers
Sharp Same-Color Cycle Covers in Two-Colored Complete Graphs
Xiao-Chuan Liu, Jonatas Teodomiro, Xu Yang
We extend the conjecture of Erdős and Gyárfás on monochromatic path covers to the setting of monochromatic cycle covers. We prove that, for all , every 2-edge-coloring of the co…
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 $χ'_…
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 e…
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…
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…