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- Title
ON THE sd<sub>b</sub>-CRITICAL GRAPHS.
- Authors
ZAMIME, MOHAMED
- Abstract
A b-coloring of a graph G is a proper coloring of its vertices such that each color class contains a vertex that has a neighbor in every other color classes. The b-chromatic number of a graph G, denoted by b(G), is the largest integer k such that G admits a b-coloring with k colors. Let Ge be the graph obtained from G by subdividing the edge e. A graph G is sdb-critical if b(Ge) < b(G) holds for any edge e of G. In this paper, we first present several basic properties of sdb-critical graphs and then we give a characterization of sdb-critical P4-sparse graphs and sdb-critical quasi-line graphs.
- Subjects
SPARSE graphs; INTEGERS; COLORS
- Publication
Transactions on Combinatorics, 2024, Vol 13, Issue 4, p363
- ISSN
2251-8657
- Publication type
Article
- DOI
10.22108/toc.2023.137558.2069