On b-perfect chordal graphs
Fr\'ed\'eric Maffray (LGS), Meriem Mechebbek
TL;DR
This paper characterizes chordal graphs where the b-chromatic number equals the chromatic number for all induced subgraphs, providing insights into their coloring properties.
Contribution
It offers a complete characterization of b-perfect chordal graphs, a class where the b-chromatic number matches the chromatic number across all induced subgraphs.
Findings
Identifies conditions for b-perfect chordal graphs
Establishes equality of b-chromatic and chromatic numbers in these graphs
Provides a structural characterization of b-perfect chordal graphs
Abstract
The b-chromatic number of a graph G is the largest integer k such that G has a coloring of the vertices in k color classes such that every color class contains a vertex that has a neighbour in all other color classes. We characterize the class of chordal graphs for which the b-chromatic number is equal to the chromatic number for every induced subgraph.
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Taxonomy
TopicsHermeneutics and Narrative Identity · Aging, Elder Care, and Social Issues · Health, Medicine and Society