Let G = (V, E) be a multigraph without loops and for any x ∈ V let E(x) be the set of edges of G incident to x. A homogeneous edge-coloring of G is an assignment of an integer m ≥ 2 and a coloring c∶ E → S of the edges of G such that ∣S∣ = m and for any x ∈ V , if ∣E(x)∣ = mq x + r x with 0 ≤ r x < m, there exists a partition of E(x) in r x color classes of cardinality q x + 1 and other m − r x color classes of cardinality q x . The homogeneous chromatic index x ̃(G) is the least m for which there exists such a coloring. We determine χ ̃ (G) in the case that G is a complete multigraph, a tree or a complete bipartite multigraph.

Homogeneous edge-colorings of graphs

BONACINI, PAOLA;CINQUEGRANI, Maria Grazia;MARINO, LUCIA MARIA
2016

Abstract

Let G = (V, E) be a multigraph without loops and for any x ∈ V let E(x) be the set of edges of G incident to x. A homogeneous edge-coloring of G is an assignment of an integer m ≥ 2 and a coloring c∶ E → S of the edges of G such that ∣S∣ = m and for any x ∈ V , if ∣E(x)∣ = mq x + r x with 0 ≤ r x < m, there exists a partition of E(x) in r x color classes of cardinality q x + 1 and other m − r x color classes of cardinality q x . The homogeneous chromatic index x ̃(G) is the least m for which there exists such a coloring. We determine χ ̃ (G) in the case that G is a complete multigraph, a tree or a complete bipartite multigraph.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/13755
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