Cooperative colorings of trees and of bipartite graphs

Ron Aharoni, Eli Berger, Maria Chudnovsky, Frédéric Havet, Zilin Jiang

Research output: Contribution to journalArticlepeer-review

Abstract

Given a system (G1, …, Gm) of graphs on the same vertex set V, a cooperative coloring is a choice of vertex sets I1, …, Im, such that Ij is independent in Gj and (formula presented)m j=1Ij = V . For a class G of graphs, let mG (d) be the minimal m such that every m graphs from G with maximum degree d have a cooperative coloring. We prove that Ω(log log d) ≤ mT (d) ≤ O(log d) and Ω(log d) ≤ mB(d) ≤ O(d/ log d), where T is the class of trees and B is the class of bipartite graphs.

Original languageEnglish
Article numberP1.41
JournalElectronic Journal of Combinatorics
Volume27
Issue number1
DOIs
StatePublished - 2020

Bibliographical note

Funding Information:
Supported in part by the United States?Israel Binational Science Foundation (BSF) grant no. 2006099, the Israel Science Foundation (ISF) grant no. 2023464 and the Discount Bank Chair at Technion. This paper is part of a project that has received funding from the European Union?s Horizon 2020 research and innovation programme, under the Marie Sklodowska-Curie grant agreement no. 823748.?Supported in part by BSF grant no. 2006099 and ISF grant no. 2023464.?Supported in part by BSF grant no. 2006099, NSF grant DMS-1550991 and US Army Research Office Grant W911NF-16-1-0404.?The work was done when Z. Jiang was a postdoctoral fellow at Technion ? Israel Institute of Technology, and was supported in part by ISF grant nos. 409/16, 936/16.

Funding Information:
∗Supported in part by the United States–Israel Binational Science Foundation (BSF) grant no. 2006099, the Israel Science Foundation (ISF) grant no. 2023464 and the Discount Bank Chair at Technion. This paper is part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme, under the Marie Sk lodowska-Curie grant agreement no. 823748. †Supported in part by BSF grant no. 2006099 and ISF grant no. 2023464. ‡Supported in part by BSF grant no. 2006099, NSF grant DMS-1550991 and US Army Research Office Grant W911NF-16-1-0404. §The work was done when Z. Jiang was a postdoctoral fellow at Technion – Israel Institute of Technology, and was supported in part by ISF grant nos. 409/16, 936/16.

Publisher Copyright:
© The authors. Released under the CC BY-ND license (International 4.0).

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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