Displaying similar documents to “About uniquely colorable mixed hypertrees”

On planar mixed hypergraphs.

Dvořák, Zdeněk, Král, Daniel (2001)

The Electronic Journal of Combinatorics [electronic only]

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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 ...

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...

Pattern hypergraphs.

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

The Electronic Journal of Combinatorics [electronic only]

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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.

Vertex-distinguishing edge-colorings of linear forests

Sylwia Cichacz, Jakub Przybyło (2010)

Discussiones Mathematicae Graph Theory

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In the PhD thesis by Burris (Memphis (1993)), a conjecture was made concerning the number of colors c(G) required to edge-color a simple graph G so that no two distinct vertices are incident to the same multiset of colors. We find the exact value of c(G) - the irregular coloring number, and hence verify the conjecture when G is a vertex-disjoint union of paths. We also investigate the point-distinguishing chromatic index, χ₀(G), where sets, instead of multisets, are required to be distinct,...