The family $D(k,m)$ of graphs having an orientation such that for every vertex $v \in V(G)$ either (outdegree) $\deg^+(v) \le k$ or (indegree) $\deg^-(v) \le m$ have been investigated recently in several papers because of the role $D(k,m)$ plays in the efforts to estimate the maximum directed cut in digraphs and the minimum cover of digraphs by directed cuts. Results concerning the chromatic number of graphs in the family $D(k,m)$ have been obtained via the notion of $d$-degeneracy of graphs. In this paper we consider a far reaching generalization of the family $D(k,m)$, in a complementary form, into the context of $r$-uniform hypergraphs, using a generalization of Hakimi's theorem to $r$-uniform hypergraphs and by showing some tight connections with the well known Ramsey numbers for hypergraphs.
@article{10_37236_2576,
author = {Yair Caro and Adriana Hansberg},
title = {Degrees in oriented hypergraphs and {Ramsey} \(p\)-chromatic number},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {3},
doi = {10.37236/2576},
zbl = {1252.05141},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2576/}
}
TY - JOUR
AU - Yair Caro
AU - Adriana Hansberg
TI - Degrees in oriented hypergraphs and Ramsey \(p\)-chromatic number
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/2576/
DO - 10.37236/2576
ID - 10_37236_2576
ER -
%0 Journal Article
%A Yair Caro
%A Adriana Hansberg
%T Degrees in oriented hypergraphs and Ramsey \(p\)-chromatic number
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/2576/
%R 10.37236/2576
%F 10_37236_2576
Yair Caro; Adriana Hansberg. Degrees in oriented hypergraphs and Ramsey \(p\)-chromatic number. The electronic journal of combinatorics, Tome 19 (2012) no. 3. doi: 10.37236/2576
