[PDF][PDF] Fractional (P, Q)-total list colorings of graphs
A Kemnitz, P Mihók, M Voigt - Discussiones Mathematicae Graph …, 2013 - sciendo.com
A Kemnitz, P Mihók, M Voigt
Discussiones Mathematicae Graph Theory, 2013•sciendo.comLet 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
(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
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
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