Block graphs - some general results and their equitable colorings

2024/02/07 by Hanna Furmańczyk, Furmańczyk, Hanna, Vahan Mkrtchyan +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2402.05289

openalex publication_date 2024/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we consider some general properties of block graphs as well as the equitable coloring problem in this class of graphs. In the first part we establish the relation between two structural parameters for general block graphs. We also give complete characterization of block graphs with given value of parameter α_min. In the next part of the paper we confirm the hypothesis for some subclass of GLS block graphs in which the problem of EQUITABLE COLORING is unlikely to be polynomial time solvable. We give also an equitable (n+2)-algorithm for all GLS block graphs. As a by product we prove that the equitable chromatic spectrum for the subclass of GLS block graphs is gap-free.

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