Sum list coloring arrays.
Isaak, Garth (2002)
The Electronic Journal of Combinatorics [electronic only]
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Isaak, Garth (2002)
The Electronic Journal of Combinatorics [electronic only]
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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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Mubayi, Dhruv (2002)
The Electronic Journal of Combinatorics [electronic only]
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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 ∆.
Hoffman, Dean G., Johnson, Peter D.jun. (2007)
International Journal of Mathematics and Mathematical Sciences
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Albertson, Michael O., Hutchinson, Joan P. (2002)
The Electronic Journal of Combinatorics [electronic only]
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Caro, Yair, Yuster, Raphael (1999)
The Electronic Journal of Combinatorics [electronic only]
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Éric Sopena, Jiaojiao Wu (2013)
Discussiones Mathematicae Graph Theory
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An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f, or the edge vw equals e or f. The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In this paper, we prove that the incidence chromatic number of the toroidal grid Tm,n = Cm2Cn equals...
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....
Arnfried Kemnitz, Peter Mihók, Margit Voigt (2013)
Discussiones Mathematicae Graph Theory
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Let r, s ∈ N, r ≥ s, and P and Q be two additive and hereditary graph properties. A (P,Q)-total (r, s)-coloring of a graph G = (V,E) is a coloring of the vertices and edges of G by s-element subsets of Zr such that for each color i, 0 ≤ i ≤ r − 1, the vertices colored by subsets containing i induce a subgraph of G with property P, the edges colored by subsets containing i induce a subgraph of G with property Q, and color sets of incident vertices and edges are disjoint. The fractional...
Schauz, Uwe (2006)
The Electronic Journal of Combinatorics [electronic only]
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Liu, Xikui, Li, Yan (2005)
International Journal of Mathematics and Mathematical Sciences
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Klazar, Martin (2008)
The Electronic Journal of Combinatorics [electronic only]
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