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Cooperative colorings of trees and of bipartite graphs
- Source :
- The Electronic Journal of Combinatorics, The Electronic Journal of Combinatorics, 2020, The Electronic Journal of Combinatorics, Open Journal Systems, 2020
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- Given a system $(G_1, \ldots ,G_m)$ of graphs on the same vertex set $V$, a cooperative coloring is a choice of vertex sets $I_1, \ldots ,I_m$, such that $I_j$ is independent in $G_j$ and $\bigcup_{j=1}^{m}I_j = V$. For a class $\mathcal{G}$ of graphs, let $m_{\mathcal{G}}(d)$ be the minimal $m$ such that every $m$ graphs from $\mathcal{G}$ with maximum degree $d$ have a cooperative coloring. We prove that $\Omega(\log\log d) \le m_\mathcal{T}(d) \le O(\log d)$ and $\Omega(\log d)\le m_\mathcal{B}(d) \le O(d/\log d)$, where $\mathcal{T}$ is the class of trees and $\mathcal{B}$ is the class of bipartite graphs.<br />Comment: 8 pages, 2 figures, accepted to the Electronic Journal of Combinatorics, corrections suggested by the referees have been incorporated
- Subjects :
- Vertex (graph theory)
05C15, 05C69
Mathematics::Commutative Algebra
Applied Mathematics
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Theoretical Computer Science
Combinatorics
Computational Theory and Mathematics
Computer Science::Discrete Mathematics
Bipartite graph
FOS: Mathematics
Discrete Mathematics and Combinatorics
Mathematics - Combinatorics
Geometry and Topology
Combinatorics (math.CO)
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 10778926
- Database :
- OpenAIRE
- Journal :
- The Electronic Journal of Combinatorics, The Electronic Journal of Combinatorics, 2020, The Electronic Journal of Combinatorics, Open Journal Systems, 2020
- Accession number :
- edsair.doi.dedup.....7eee996f0f735124f87101c7d8beb5ec