Cooperative colorings of trees and of bipartite graphs

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

doi:10.37236/8111

Cooperative colorings of trees and of bipartite graphs

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

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Given a system (G₁, …, G_m) of graphs on the same vertex set V, a cooperative coloring is a choice of vertex sets I₁, …, I_m, such that I_j is independent in G_j and (formula presented)_m j=1^Ij = 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(log log 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.

Original language	English (US)
Article number	P1.41
Journal	Electronic Journal of Combinatorics
Volume	27
Issue number	1
DOIs	https://doi.org/10.37236/8111
State	Published - 2020

All Science Journal Classification (ASJC) codes

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

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title = "Cooperative colorings of trees and of bipartite graphs",

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.",

author = "Ron Aharoni and Eli Berger and Maria Chudnovsky and Fr{\'e}d{\'e}ric Havet and Zilin Jiang",

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T1 - Cooperative colorings of trees and of bipartite graphs

AU - Aharoni, Ron

AU - Berger, Eli

AU - Chudnovsky, Maria

AU - Havet, Frédéric

AU - Jiang, Zilin

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

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Cooperative colorings of trees and of bipartite graphs

Abstract

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