Results 31 to 40 of about 700 (120)
Fractional Turan's theorem and bounds for the chromatic number
Electronic Notes in Discrete Mathematics, 2015 Abstract Turan's theorem gives conditions for finding large complete subgraphs in a graph in terms of the number of edges. In this work we look for families of graphs in which there is a similar theorem, but which will allow us to find larger complete subgraphs.
Leonardo Martínez-Sandoval +1 more
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An eigenvalue bound for the fractional chromatic number
, 2021 We show that Hoffman's sum of eigenvalues bound for the chromatic number is at least as good as the Lovász theta number, but no better than the ceiling of the fractional chromatic number. In order to do so, we display an interesting connection between this sum of eigenvalues bound and a generalization of the Lovász theta number introduced by Manber and
Silva, Marcel K. de Carli +2 more
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Random independent sets in triangle-free graphs
Forum of Mathematics, SigmaWe establish several new results on the existence of probability distributions on the independent sets in triangle-free graphs where each vertex is present with a given probability.
Anders Martinsson, Raphael Steiner
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On Coloring of Fractional Powers of Star, Wheel, Friendship, and Fan Graphs
Indonesian Journal of CombinatoricsLet G be a simple, connected, and undirected graph. For m, n ∈ ℕ, the fractional power Gm/n = (G1/n)m of G is constructed by taking the n-subdivision of G (replacing each edge by a path of length n), and then raising the resulting graph to the m-th power
Farisan Hafizh +4 more
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On the fractional chromatic number and the lexicographic product of graphs
Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The fractional chromatic number of the plane is at least 4
, 2023 We prove that the fractional chromatic number $χ_f(\mathbb R^2)$ of the unit distance graph of the Euclidean plane is greater than or equal to $4$. Interestingly, however, we cannot present a finite subgraph $G$ of the plane such that $χ_f(G)\ge 4$.
Matolcsi, Máté +3 more
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Critical Subgraphs of Schrijver Graphs for the Fractional Chromatic Number
Graphs and CombinatoricsAbstractSchrijver graphs are vertex-color-critical subgraphs of Kneser graphs having the same chromatic number. They also share the value of their fractional chromatic number but Schrijver graphs are not critical for that. Here we present an induced subgraph of every Schrijver graph that is vertex-critical with respect to the fractional chromatic ...
Anna Gujgiczer, Gábor Simonyi
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Ars Mathematica Contemporanea, 2010 The r -inflation of a graph G is the lexicographic product G with K r . A graph is said to have thickness t if its edges can be partitioned into t sets, each of which induces a planar graph, and t is smallest possible. In the setting of the r -inflation of planar graphs, we investigate the generalization of Ringel's famous Earth-Moon ...
Michael O. Albertson +2 more
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On the Fractional Chromatic Number of Monotone Self-dual Boolean Functions
Discrete Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daya Ram Gaur, Kazuhisa Makino
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The fractional chromatic number of the direct product of graphs [PDF]
Glasgow Mathematical Journal, 2002 This paper discusses the fractional chromatic number of the direct product of graphs. It is proved that if H is a circulant graph G^k_d, or a Kneser graph, or a direct sum of such graphs, then for any graph G, \chi_f{\hskip1}(G\times H{\hskip1}) = {\text min}\{\chi_f{\hskip1}(G), \chi_f{\hskip1}(H{\hskip1})\}.
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