Cooperative colorings of trees and of bipartite graphs
ELECTRONIC JOURNAL OF COMBINATORICS(2018)
摘要
Given a system (G_1, … ,G_m) of graphs on the same vertex set V, a cooperative coloring is a choice of vertex sets I_1, … ,I_m, such that I_j is independent in G_j and ⋃_j=1^mI_j = V. For a class 𝒢 of graphs, let m_𝒢(d) be the minimal m such that every m graphs from 𝒢 with maximum degree d have a cooperative coloring. We prove that Ω(loglog d) ≤ m_𝒯(d) ≤ O(log d) and Ω(log d)≤ m_ℬ(d) ≤ O(d/log d), where 𝒯 is the class of trees and ℬ is the class of bipartite graphs.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络