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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Displaying similar documents to “The Incidence Chromatic Number of Toroidal Grids”
Coloring with no 2-colored 's.
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 ∆.
On swell-colored complete graphs.
Ward, C., Szabó, S. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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The set chromatic number of a graph
Gary Chartrand, Futaba Okamoto, Craig W. Rasmussen, Ping Zhang (2009)
Discussiones Mathematicae Graph Theory
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For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs...
Graph color extensions: When Hadwiger's conjecture and embeddings help.
Albertson, Michael O., Hutchinson, Joan P. (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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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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The circular chromatic index of flower snarks.
Ghebleh, Mohammad, Kral', Daniel, Norine, Serguei, Thomas, Robin (2006)
The Electronic Journal of Combinatorics [electronic only]
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Neochromatica
Panagiotis Cheilaris, Ernst Specker, Stathis Zachos (2010)
Commentationes Mathematicae Universitatis Carolinae
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We create and discuss several modifications to traditional graph coloring. In particular, we classify various notions of coloring in a proper hierarchy. We concentrate on grid graphs whose colorings can be represented by natural number entries in arrays with various restrictions.
Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs
P. Francis, S. Francis Raj (2016)
Discussiones Mathematicae Graph Theory
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A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be...
On Monochromatic Subgraphs of Edge-Colored Complete Graphs
Eric Andrews, Futaba Fujie, Kyle Kolasinski, Chira Lumduanhom, Adam Yusko (2014)
Discussiones Mathematicae Graph Theory
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In a red-blue coloring of a nonempty graph, every edge is colored red or blue. If the resulting edge-colored graph contains a nonempty subgraph G without isolated vertices every edge of which is colored the same, then G is said to be monochromatic. For two nonempty graphs G and H without isolated vertices, the mono- chromatic Ramsey number mr(G,H) of G and H is the minimum integer n such that every red-blue coloring of Kn results in a monochromatic G or a monochromatic H. Thus, the standard...