Results 21 to 30 of about 700 (120)
A parallel lagrangian heuristic for the fractional chromatic number of a graph
RAIRO - Operations Research, 2023 We propose a new integer programming formulation for the Fractional Chromatic Number Problem. The formulation is based on representatives of stable sets. In addition, we present a Lagrangian heuristic from a Lagrangian relaxation of this formulation to obtain a good feasible solution for the problem.
Paulo Henrique Macêdo de Araújo +2 more
openaire +1 more source
Fractional Aspects of the Erdős-Faber-Lovász Conjecture
Discussiones Mathematicae Graph Theory, 2015 The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n.
Bosica John, Tardif Claude
doaj +1 more source
Estimating the fractional chromatic number of a graph [PDF]
Acta Universitatis Sapientiae, Informatica, 2021 Abstract The fractional chromatic number of a graph is defined as the optimum of a rather unwieldy linear program. (Setting up the program requires generating all independent sets of the given graph.) Using combinatorial arguments we construct a more manageable linear program whose optimum value provides an upper estimate for the ...
openaire +2 more sources
The fractional chromatic number of Zykov products of graphs
Applied Mathematics Letters, 2011 Zykov designed one of the oldest known families of triangle-free graphs with arbitrarily high chromatic number. We determine the fractional chromatic number of the Zykov product of a family of graphs. As a corollary, we deduce that the fractional chromatic numbers of the Zykov graphs satisfy the same recurrence relation as those of the Mycielski graphs,
Charbit, Pierre, Sereni, Jean-Sébastien
openaire +3 more sources
Fractional Q-Edge-Coloring of Graphs
Discussiones Mathematicae Graph Theory, 2013 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.
Czap Július, Mihók Peter
doaj +1 more source
Generalized Fractional and Circular Total Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2015 Let P and Q be additive and hereditary graph properties, r, s ∈ N, r ≥ s, and [ℤr]s be the set of all s-element subsets of ℤr. An (r, s)-fractional (P,Q)-total coloring of G is an assignment h : V (G) ∪ E(G) → [ℤr]s such that for each i ∈ ℤr the ...
Kemnitz Arnfried +4 more
doaj +1 more source
Generalized Fractional Total Colorings of Complete Graph
Discussiones Mathematicae Graph Theory, 2013 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,
Karafová Gabriela
doaj +1 more source
Generalized Fractional Total Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2015 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, . . .
Karafová Gabriela, Soták Roman
doaj +1 more source
The fractional chromatic number of triangle-free subcubic graphs [PDF]
European Journal of Combinatorics, 2014 Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 (which is roughly 2.909).
David G. Ferguson +2 more
openaire +3 more sources
Fractional (P,Q)-Total List Colorings of Graphs
Discussiones Mathematicae Graph Theory, 2013 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 ...
Kemnitz Arnfried +2 more
doaj +1 more source