Displaying similar documents to “Gaps in the chromatic spectrum of face-constrained plane graphs.”

On planar mixed hypergraphs.

Dvořák, Zdeněk, Král, Daniel (2001)

The Electronic Journal of Combinatorics [electronic only]

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About uniquely colorable mixed hypertrees

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...

Chromatic Polynomials of Mixed Hypercycles

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 ...

Pattern hypergraphs.

Dvořák, Zdeněk, Kára, Jan, Král', Daniel, Pangrác, Ondřej (2010)

The Electronic Journal of Combinatorics [electronic only]

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Constrained Colouring and σ-Hypergraphs

Yair Caro, Josef Lauri, Christina Zarb (2015)

Discussiones Mathematicae Graph Theory

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A constrained colouring or, more specifically, an (α, β)-colouring of a hypergraph H, is an assignment of colours to its vertices such that no edge of H contains less than α or more than β vertices with different colours. This notion, introduced by Bujtás and Tuza, generalises both classical hypergraph colourings and more general Voloshin colourings of hypergraphs. In fact, for r-uniform hypergraphs, classical colourings correspond to (2, r)-colourings while an important instance of...

Lower bounds for the colored mixed chromatic number of some classes of graphs

Ruy Fabila Monroy, D. Flores, Clemens Huemer, A. Montejano (2008)

Commentationes Mathematicae Universitatis Carolinae

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A colored mixed graph has vertices linked by both colored arcs and colored edges. The chromatic number of such a graph G is defined as the smallest order of a colored mixed graph H such that there exists a (color preserving) homomorphism from G to H . These notions were introduced by Nešetřil and Raspaud in , J. Combin. Theory Ser. B (2000), no. 1, 147–155, where the exact chromatic number of colored mixed trees was given. We prove here that this chromatic number is reached by the much...

Three edge-coloring conjectures

Richard H. Schelp (2002)

Discussiones Mathematicae Graph Theory

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The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.