Results 101 to 110 of about 139 (132)
Adapted List Coloring of Graphs and Hypergraphs [PDF]
SIAM Journal on Discrete Mathematics, 2008 We introduce and study adapted list coloring of graphs and hypergraphs. This is a generalization of ordinary list coloring and adapted coloring, and has more applications than these. We prove that the upper bounds on the adaptable choosability of graphs and uniform hypergraphs in terms of maximum degree are sufficiently stronger than those on the ...
Alexandr Kostochka, Xuding Zhu
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On splittable colorings of graphs and hypergraphs [PDF]
Journal of Graph Theory, 2002 AbstractThe notion of a split coloring of a complete graph was introduced by Erdős and Gyárfás [7] as a generalization of split graphs. In this work, we offer an alternate interpretation by comparing such a coloring to the classical Ramsey coloring problem via a two‐round game played against an adversary.
Zoltan Furedi
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Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs [PDF]
European Journal of Combinatorics, 2019 9 ...
József Balogh +2 more
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Dimension, Graph and Hypergraph Coloring
Order, 2000A linear extension \(L\) of a poset \(P\) reverses an incomparable pair \((x,y)\) of \(P\) if \(x>y\) in \(L\). A set \(S\) of incomparable pairs forms a strict alternating cycle of \(P\) if no linear extension of \(P\) reverses all pairs in \(S\) but for all \(T \subset S\) there is a linear extension of \(P\) which reverses all pairs in \(T\).
Stefan Felsner, William T. Trotter
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Unique-Maximum and Conflict-Free Coloring for Hypergraphs and Tree Graphs [PDF]
Lecture Notes in Computer Science, 2012 We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color appears only once. In a conflict-free coloring, in every hyperedge of the hypergraph there is a color
Panagiotis Cheilaris +2 more
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On hypergraph coloring and 3-uniform linear hypergraph set-indexers of a graph
Discrete Mathematics, Algorithms and Applications, 2015For a graph G = (V, E) and a nonempty set X, a linear hypergraph set-indexer (LHSI) is a function f : V(G) → 2X satisfying the following conditions: (i) f is injective (ii) the ordered pair Hf(G) = (X, f(V)), where f(V) = {f(v) : v ∈ V(G)}, is a linear hypergraph (iii) the induced function f⊕ : E → 2X defined by f⊕(uv) = f(u) ⊕ f(v), for all uv ∈ E is
Viji Paul, K. Augustine Germina
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Uniform hypergraphs with many edge‐colorings avoiding a fixed rainbow expanded complete graph
Journal of Graph Theory, 2021AbstractFor fixed positive integers and , and a fixed ‐uniform hypergraph , we look for ‐vertex hypergraphs that admit the maximum number of ‐edge‐colorings with the property that there is no copy of for which all hyperedges are assigned different colors. We consider , the ‐uniform expanded complete graph, and we prove that the Turán hypergraph , the
Lucas de Oliveira Contiero +3 more
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Sparse color‐critical graphs and hypergraphs with no short cycles
Journal of Graph Theory, 1994AbstractWe give constructions of color‐critical graphs and hypergraphs with no short cycles and with relatively few edges. In particular, we show that, for each n ≧ 3, the smallest number of edges in a 3‐critical triangle‐free n‐graph (hypergraph) with m vertices is m + o(m) as m → ∞.
H. L. Abbott +2 more
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Coloring number and on-line Ramsey theory for graphs and hypergraphs
Combinatorica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hal A. Kierstead, Goran Konjevod
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ON k-LOCAL AND k-MEAN COLORINGS OF GRAPHS AND HYPERGRAPHS
The Quarterly Journal of Mathematics, 1993In the paper, \(k\)-local and \(k\)-mean colorings of graphs and hypergraphs are studied. Given an edge-coloring \(f\) and a vertex \(v\), \(\alpha_ f(v)\) denotes the number of distinct colors that appear on the edges incident with \(v\). A coloring \(f\) is \(k\)-local if for every vertex \(v\), \(\alpha_ f(v) \leq k\). A coloring \(f\) is \(k\)-mean
Caro, Yair, Tuza, Zsolt
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