Equitable colorings of $K_4$-minor-free graphs
Copyright policy )Equitable colorings of $K_4$-minor-free graphs
We demonstrate that for every positive integer $\Delta$, every $K_4$-minor-free graph with maximum degree $\Delta$ admits an equitable coloring with $k$ colors where $k\ge\frac{\Delta+3}{2}$. This bound is tight and confirms a conjecture by Zhang and Wu. We do not use the discharging method but rather exploit decomposition trees of $K_4$-minor-free graphs.
K_4-minor-free graph, equitable coloring, maximum degree, series-parallel graph, \(K_4\)-minor-free graph, Graph minors, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Coloring of graphs and hypergraphs, Graph algorithms (graph-theoretic aspects), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
K_4-minor-free graph, equitable coloring, maximum degree, series-parallel graph, \(K_4\)-minor-free graph, Graph minors, [MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO], Coloring of graphs and hypergraphs, Graph algorithms (graph-theoretic aspects), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)
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