Geodesic
Pattern hypergraphs
The electronic journal of combinatorics, Tome 17 (2010)
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The notion of pattern hypergraph provides a unified view of several previously studied coloring concepts. A pattern hypergraph $H$ is a hypergraph where each edge is assigned a type $\Pi_i$ that determines which of possible colorings of the edge are proper. A vertex coloring of $H$ is proper if it is proper for every edge. In general, the set of integers $k$ such that $H$ can be properly colored with exactly $k$ colors need not be an interval. We find a simple sufficient and necessary condition on the edge types $\Pi_1,\ldots,\Pi_\lambda$ for the existence of a pattern hypergraph $H$ with edges of types $\Pi_1,\ldots,\Pi_\lambda$ such that the numbers of colors in proper colorings of $H$ do not form an interval of integers.
DOI : 10.37236/287
Classification : 05C15, 05C65
Mots-clés : pattern hypergraph, coloring concept, proper coloring 
@article{10_37236_287,
     author = {Zden\v{e}k Dvo\v{r}\'ak and Jan K\'ara and Daniel Kr\'al' and Ond\v{r}ej Pangr\'ac},
     title = {Pattern hypergraphs},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/287},
     zbl = {1193.05076},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/287/}
}
TY  - JOUR
AU  - Zdeněk Dvořák
AU  - Jan Kára
AU  - Daniel Král'
AU  - Ondřej Pangrác
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JO  - The electronic journal of combinatorics
PY  - 2010
VL  - 17
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DO  - 10.37236/287
ID  - 10_37236_287
ER  - 
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%A Jan Kára
%A Daniel Král'
%A Ondřej Pangrác
%T Pattern hypergraphs
%J The electronic journal of combinatorics
%D 2010
%V 17
%U http://geodesic.mathdoc.fr/articles/10.37236/287/
%R 10.37236/287
%F 10_37236_287
Zdeněk Dvořák; Jan Kára; Daniel Král'; Ondřej Pangrác. Pattern hypergraphs. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/287

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