Fractional (P,Q)-Total List Colorings of Graphs

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 χ′′ f,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.

Keywords

• graph property
• total coloring
• (p,q)-total coloring
• fractional coloring
• fractional (p,q)-total chromatic number
• circular coloring
• circular (p,q)-total chromatic number
• list coloring
• (p,q)-total (a
• b)-list colorings