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Degrees in oriented hypergraphs and Ramsey p-chromatic number
Caro, Y.; Hansberg Pastor, Adriana
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
The family D(k,m) of graphs having an orientation such that for every vertex v ∈ V (G) either (outdegree) deg+(v) ≤ k or (indegree) deg−(v) ≤ 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
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Graph theory
Chromatic number
D-degenerate hy- pergraph
Oriented hypergraphs
Ramsey numbers
Ramsey p-chromatic number
Grafs, Teoria de
05C Teoria de grafs
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
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