(P,Q)-Total (r,s)-colorings of graphs Artikel uri icon

Open Access

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Peer Reviewed

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Abstract

  • Let r,s∈N, r≥s, and P and Q be two additive and hereditary graph properties. A (P,Q)-total (r,s)-coloring of a graph G=(V,E) is a coloring of the vertices and edges of G by s-element subsets of Zr such that for each color i, 0≤i≤r−1, the vertices colored by subsets containing i induce a subgraph of G with property P, the edges colored by subsets containing i induce a subgraph of G with property Q, and color sets of incident vertices and edges are disjoint. The fractional (P,Q)-total chromatic number χf,P,Q″(G) of  G is defined as the infimum of all ratios r/s such that G has a (P,Q)-total (r,s)-coloring. In this paper we present general lower and upper bounds for χf,P,Q″(G) and also give some exact values for specific properties and specific classes of graphs.

Veröffentlichungszeitpunkt

  • Juni 10, 2015