Colouring planar mixed hypergraphs.
Kündgen, André, Mendelsohn, Eric, Voloshin, Vitaly (2000)
The Electronic Journal of Combinatorics [electronic only]
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Kündgen, André, Mendelsohn, Eric, Voloshin, Vitaly (2000)
The Electronic Journal of Combinatorics [electronic only]
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Král, Daniel (2004)
The Electronic Journal of Combinatorics [electronic only]
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Kobler, Daniel, Kündgen, André (2001)
The Electronic Journal of Combinatorics [electronic only]
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Dvořák, Zdeněk, Kára, Jan, Král', Daniel, Pangrác, Ondřej (2010)
The Electronic Journal of Combinatorics [electronic only]
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Julian A. Allagan, David Slutzky (2014)
Discussiones Mathematicae Graph Theory
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We color the vertices of each of the edges of a C-hypergraph (or cohypergraph) in such a way that at least two vertices receive the same color and in every proper coloring of a B-hypergraph (or bihypergraph), we forbid the cases when the vertices of any of its edges are colored with the same color (monochromatic) or when they are all colored with distinct colors (rainbow). In this paper, we determined explicit formulae for the chromatic polynomials of C-hypercycles and B-hypercycles ...
LeSaulnier, Timothy D., Stocker, Christopher, Wenger, Paul S., West, Douglas B. (2010)
The Electronic Journal of Combinatorics [electronic only]
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Angela Niculitsa, Vitaly Voloshin (2000)
Discussiones Mathematicae Graph Theory
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A mixed hypergraph is a triple 𝓗 = (X,𝓒,𝓓) where X is the vertex set and each of 𝓒, 𝓓 is a family of subsets of X, the 𝓒-edges and 𝓓-edges, respectively. A k-coloring of 𝓗 is a mapping c: X → [k] such that each 𝓒-edge has two vertices with the same color and each 𝓓-edge has two vertices with distinct colors. 𝓗 = (X,𝓒,𝓓) is called a mixed hypertree if there exists a tree T = (X,𝓔) such that every 𝓓-edge and every 𝓒-edge induces a subtree of T. A mixed hypergraph 𝓗 is...
Ghebleh, Mohammad, Kral', Daniel, Norine, Serguei, Thomas, Robin (2006)
The Electronic Journal of Combinatorics [electronic only]
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Július Czap, Zsolt Tuza (2013)
Discussiones Mathematicae Graph Theory
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An edge coloring of a plane graph G is facially proper if no two faceadjacent edges of G receive the same color. A facial (facially proper) parity edge coloring of a plane graph G is an (facially proper) edge coloring with the property that, for each color c and each face f of G, either an odd number of edges incident with f is colored with c, or color c does not occur on the edges of f. In this paper we deal with the following question: For which integers k does there exist a facial...
Juvan, Martin, Mohar, Bojan, Thomas, Robin (1999)
The Electronic Journal of Combinatorics [electronic only]
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Fujita, Shinya, Kaneko, Atsushi, Schiermeyer, Ingo, Suzuki, Kazuhiro (2009)
The Electronic Journal of Combinatorics [electronic only]
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Loh, Po-Shen (2009)
The Electronic Journal of Combinatorics [electronic only]
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Yuehua Bu, Ko-Wei Lih, Weifan Wang (2011)
Discussiones Mathematicae Graph Theory
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An adjacent vertex distinguishing edge-coloring of a graph G is a proper edge-coloring o G such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing edge-coloring of G is denoted by χ'ₐ(G). We prove that χ'ₐ(G) is at most the maximum degree plus 2 if G is a planar graph without isolated edges whose girth is at least 6. This gives new evidence to a conjecture proposed in [Z. Zhang, L. Liu,...
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 ∆.