We investigate the relations among the chromatic index q(H), the maximum degree Δ(H), the total chromatic number q*(H), and the maximum size Δ0(H) of an intersecting subhypergraph of a hypergraph H. For some particular classes of hypergraphs, including Steiner systems, we provide sufficient conditions insuring that some (or all) of the trivial inequalities Δ(H)≤Δ0(H)≤q(H)≤q*(H turn to equality. For instance, we prove that Δ(H)= Δ0(H) holds whenever the maximum degree of a hypergraph H is sufficiently large with respect to the rank and the 'pair-degree' of H.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics