Results 101 to 110 of about 700 (120)
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Fractional chromatic numbers of cones over graphs
Journal of Graph Theory, 2001AbstractWe introduce a construction called the cone over a graph. It is a natural generalisation of Mycielski's construction. We give a formula for the fractional chromatic numbers of all cones over graphs, which generalizes that given in 3 for Mycielski's construction. © 2001 John Wiley & Sons, Inc.
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Fractional chromatic numbers of tensor products of three graphs
Discrete Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jimeng Xiao, Shenggui Zhang
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The fractional chromatic number of mycielski's graphs
Journal of Graph Theory, 1995AbstractJames ProppThe most familiar construction of graphs whose clique number is much smaller than their chromatic number is due to Mycielski, who constructed a sequence Gn of triangle‐free graphs with X(Gn) = n. In this article, we calculate the fractional chromatic number of Gn and show that this sequence of numbers satisfies the unexpected ...
Michael Larsen +2 more
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Fractional Chromatic Numbers and Chromatic Numbers for the Fibonacci Distance Graphs
The Fibonacci Quarterlyexaly +2 more sources
Counterexamples to Hedetniemi’s Conjecture with Large Fractional Chromatic Numbers
Graphs and Combinatorics, 2022Let \(G \times H\) be the direct product (also called categorical or tensor product) of the graphs \(G\) and \(H\), which is the graph with \(V( G \times H)=V(G) \times V(H)\) and adjacencies \((u,v) \sim (u^\prime,v^\prime)\) if \(u \sim u^\prime\) and \(v \sim v^\prime\).
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The fractional chromatic number of infinite graphs
Journal of Graph Theory, 1995AbstractThe fractional chromatic number of a graph G is the infimum of the total weight that can be assigned to the independent sets of G in such a way that, for each vertex v of G, the sum of the weights of the independent sets containing v is at least 1.In this note we give a graph a graph whose fractional chromatic number is strictly greater than ...
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The Fractional Chromatic Number Of The Categorical Product Of Graphs
Combinatorica, 2005We prove that the identity $$\chi _{f} ( G \times H ) \geqslant \frac{1}{4} \cdot \min \{ \chi _{f} ( G ),\chi _{f} ( H ) \}$$ holds for all directed graphs G and H. Similar bounds for the usual chromatic number seem to be much harder to obtain: It is still not known whether there exists a number n such that χ(G×H) ≥ 4 for all directed graphs G, H with
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The fractional chromatic number of $K_Δ$-free graphs
2021For a simple graph $G$, let $χ_f(G)$ be the fractional chromatic number of $G$. In this paper, we aim to establish upper bounds on $χ_f(G)$ for those graphs $G$ with restrictions on the clique number. Namely, we prove that for $Δ\geq 4$, if $G$ has maximum degree at most $Δ$ and is $K_Δ$-free, then $χ_f(G) \leq Δ-\tfrac{1}{8}$ unless $G= C^2_8$ or $G =
Hu, Xiaolan, Peng, Xing
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Bounding the fractional chromatic number of $K_Δ$-free graphs
CoRR, 201230 pages, revised ...
Katherine Edwards, Andrew D. King
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Fractional DP-chromatic number of planar graphs of large girth
Discrete Mathematics, Algorithms and Applications, 2021This paper proves that for any integer [Formula: see text], every planar graph [Formula: see text] of girth at least [Formula: see text] has fractional DP-chromatic number at most [Formula: see text].
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