New sharp lower bound for the quorum coloring number of trees
•The alliance partition number of a tree has a new sharp lower bound computable in linear time.•This new lower bound is better than all those that have been previously established.•There is a relationship between the order, the diameter, the vertices degree and the matching number of a subgraph of a...
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| Veröffentlicht in: | Information processing letters Jg. 178; S. 106297 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
01.11.2022
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| Schlagworte: | |
| ISSN: | 0020-0190, 1872-6119 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | •The alliance partition number of a tree has a new sharp lower bound computable in linear time.•This new lower bound is better than all those that have been previously established.•There is a relationship between the order, the diameter, the vertices degree and the matching number of a subgraph of a tree.•The alliance partition number of a binary tree is computable in linear time.
A partition π={V1,V2,...,Vk} of the vertex set V of a graph G into k color classes Vi, with 1≤i≤k is called a quorum coloring if for every vertex v∈V, at least half of the vertices in the closed neighborhood N[v] of v have the same color as v. The maximum cardinality of a quorum coloring of G is called the quorum coloring number of G and is denoted by ψq(G). A quorum coloring of order ψq(G) is a ψq-coloring. In this paper, we partially answer an open problem concerning quorum colorings of graphs. Namely, we improve a sharp lower bound given in 2012 by Eroh and Gera on the quorum coloring number of a nontrivial tree, and show that our new lower bound can be computed in linear time. Moreover, we show that this bound is attained by all non trivial binary trees. |
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| ISSN: | 0020-0190 1872-6119 |
| DOI: | 10.1016/j.ipl.2022.106297 |