Displaying similar documents to “On feasible sets of mixed hypergraphs.”

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...

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 ...

Pattern hypergraphs.

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

The Electronic Journal of Combinatorics [electronic only]

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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...

A Note on Neighbor Expanded Sum Distinguishing Index

Evelyne Flandrin, Hao Li, Antoni Marczyk, Jean-François Saclé, Mariusz Woźniak (2017)

Discussiones Mathematicae Graph Theory

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A total k-coloring of a graph G is a coloring of vertices and edges of G using colors of the set [k] = {1, . . . , k}. These colors can be used to distinguish the vertices of G. There are many possibilities of such a distinction. In this paper, we consider the sum of colors on incident edges and adjacent vertices.