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Proper edge coloring of subcubic graphs with rainbow C4-s
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A proper edge-coloring of a graph is called a B-coloring if every 4-cycle receives four distinct colors. Let qB(G) denote the minimum number of colors required for a B-coloring of a graph G. Motivated by earlier work related to the (7,4)-problem and subsequent studies on upper bounds for qB(G), we investigate this parameter for graphs of maximum degree three. We show that every subcubic graph G distinct from K3,3 satisfies qB(G) ≤ 6, and that this bound is best possible. Moreover, we provide a complete characterization of the subcubic graphs for which equality holds.
Title: Proper edge coloring of subcubic graphs with rainbow C4-s
Description:
A proper edge-coloring of a graph is called a B-coloring if every 4-cycle receives four distinct colors.
Let qB(G) denote the minimum number of colors required for a B-coloring of a graph G.
Motivated by earlier work related to the (7,4)-problem and subsequent studies on upper bounds for qB(G), we investigate this parameter for graphs of maximum degree three.
We show that every subcubic graph G distinct from K3,3 satisfies qB(G) ≤ 6, and that this bound is best possible.
Moreover, we provide a complete characterization of the subcubic graphs for which equality holds.
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