Generalized Fractional and Circular Total Colorings of Graphs

Arnfried Kemnitz; Massimiliano Marangio; Peter Mihók; Janka Oravcová; Roman Soták

The search session has expired. Please query the service again.

Displaying similar documents to “Generalized Fractional and Circular Total Colorings of Graphs”

Generalized Fractional Total Colorings of Graphs

Gabriela Karafová, Roman Soták (2015)

Discussiones Mathematicae Graph Theory

Similarity:

Let P and Q be additive and hereditary graph properties and let r, s be integers such that r ≥ s. Then an r/s -fractional (P,Q)-total coloring of a finite graph G = (V,E) is a mapping f, which assigns an s-element subset of the set {1, 2, . . . , r} to each vertex and each edge, moreover, for any color i all vertices of color i induce a subgraph with property P, all edges of color i induce a subgraph with property Q and vertices and incident edges have been assigned disjoint sets of...

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

Arnfried Kemnitz, Peter Mihók, Margit Voigt (2013)

Discussiones Mathematicae Graph Theory

Similarity:

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...

Generalized Fractional Total Colorings of Complete Graph

Gabriela Karafová (2013)

Discussiones Mathematicae Graph Theory

Similarity:

An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be two additive and hereditary graph properties and let r, s be integers such that r ≥ s Then an [...] fractional (P,Q)-total coloring of a finite graph G = (V,E) is a mapping f, which assigns an s-element subset of the set {1, 2, . . . , r} to each vertex and each edge, moreover, for any color i all vertices of color i induce a subgraph of property...

Fractional Q-Edge-Coloring of Graphs

Július Czap, Peter Mihók (2013)

Discussiones Mathematicae Graph Theory

Similarity:

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let [...] be an additive hereditary property of graphs. A [...] -edge-coloring of a simple graph is an edge coloring in which the edges colored with the same color induce a subgraph of property [...] . In this paper we present some results on fractional [...] -edge-colorings. We determine the fractional [...] -edge chromatic number for matroidal properties of...

The non-crossing graph.

Linial, Nathan, Saks, Michael, Statter, David (2006)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

The chromatic number of the product of two graphs is at least half the minimum of the fractional chromatic numbers of the factors

Claude Tardif (2001)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

One consequence of Hedetniemi’s conjecture on the chromatic number of the product of graphs is that the bound $χ (G \times H) \geq min {χ_{f} (G), χ_{f} (H)}$ should always hold. We prove that $χ (G \times H) \geq \frac{1}{2} min {χ_{f} (G), χ_{f} (H)}$ .

The set chromatic number of a graph

Gary Chartrand, Futaba Okamoto, Craig W. Rasmussen, Ping Zhang (2009)

Discussiones Mathematicae Graph Theory

Similarity:

For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs...

Fractional biclique covers and partitions of graphs.

Watts, Valerie L. (2006)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs

P. Francis, S. Francis Raj (2016)

Discussiones Mathematicae Graph Theory

Similarity:

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be...

Coloring with no 2-colored $P_{4}$ 's.

Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)

The Electronic Journal of Combinatorics [electronic only]

Similarity: