On a theorem of Erdős, Rubin, and Taylor on choosability of complete bipartite graphs.
Kostochka, Alexandr (2002)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “A paintability version of the combinatorial Nullstellensatz, and list colorings of -partite -uniform hypergraphs.”
On a theorem of Erdős, Rubin, and Taylor on choosability of complete bipartite graphs.
Mr. Paint and Mrs. Correct.
Schauz, Uwe (2009)
The Electronic Journal of Combinatorics [electronic only]
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Coloring with no 2-colored 's.
Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)
The Electronic Journal of Combinatorics [electronic only]
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Precoloring extension with fixed color bound.
Kratochvíl, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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A linear upper bound in zero-sum Ramsey theory.
Caro, Yair (1994)
International Journal of Mathematics and Mathematical Sciences
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Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Oleg V. Borodin, Anna O. Ivanova (2013)
Discussiones Mathematicae Graph Theory
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We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40 [...] +1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Colorings and orientations of matrices and graphs.
Schauz, Uwe (2006)
The Electronic Journal of Combinatorics [electronic only]
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Flexible color lists in Alon and Tarsi's theorem, and time scheduling with unreliable participants.
Schauz, Uwe (2010)
The Electronic Journal of Combinatorics [electronic only]
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On colorings avoiding a rainbow cycle and a fixed monochromatic subgraph.
Axenovich, Maria, Choi, JiHyeok (2010)
The Electronic Journal of Combinatorics [electronic only]
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Backbone colorings along stars and matchings in split graphs: their span is close to the chromatic number
Hajo Broersma, Bert Marchal, Daniel Paulusma, A.N.M. Salman (2009)
Discussiones Mathematicae Graph Theory
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We continue the study on backbone colorings, a variation on classical vertex colorings that was introduced at WG2003. Given a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring for G and H is a proper vertex coloring V→ {1,2,...} of G in which the colors assigned to adjacent vertices in H differ by at least λ. The algorithmic and combinatorial properties of backbone colorings have been studied for various types of backbones in a number of papers....
Generalizing the Ramsey problem through diameter.
Mubayi, Dhruv (2002)
The Electronic Journal of Combinatorics [electronic only]
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An improvement to Mathon's cyclotomic Ramsey colorings.
Xu, Xiaodong, Radziszowski, Stanislaw P. (2009)
The Electronic Journal of Combinatorics [electronic only]
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A Tight Bound on the Set Chromatic Number
Jean-Sébastien Sereni, Zelealem B. Yilma (2013)
Discussiones Mathematicae Graph Theory
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We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that χs(G) > ⌈log2 χ(G)⌉ + 1, where χs(G) and χ(G) are the set chromatic number and the chromatic number of G, respectively. This answers in the affirmative a conjecture of Gera, Okamoto, Rasmussen and Zhang.
Rainbow matching in edge-colored graphs.
LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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