A De Bruijn–Erdős theorem for chordal graphs

International audienceA special case of a combinatorial theorem of De Bruijn and Erd˝ os asserts that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvátal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces induced by connected chordal graphs

Intersperse Coloring

the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. In this thesis, we introduce the intersperse coloring problem, which is a generalized version of the hypergraph coloring problem. In the intersperse coloring problem, we seek a coloring that assigns at least ℓ different colors to each hyperedge of the input hypergraph, where ℓ is an input parameter of the problem. We show that the notion of intersperse coloring unifies several well-known coloring problems, in addition to the conventional graph and hypergraph coloring problems, such as the strong coloring of hypergraphs, the star coloring problem, the problem of proper coloring of graph powers, the acyclic coloring problem, and the frugal coloring problem. We also provide a number of upper and lower bounds on the intersperse coloring problem on hypergraphs in the general case. The nice thing about our general bounds is that they can be applied to all the coloring problems that are specia

A de Bruijn - Erdos theorem and metric spaces

Combinatoric