On neighborhood-Helly graphs

  title={On neighborhood-Helly graphs},
  author={Marina Groshaus and Min Chih Lin and Jayme Luiz Szwarcfiter},
  journal={Discrete Applied Mathematics},
A family F of subsets of some set is intersecting when sets of F pairwise intersect. The family F is Helly when every intersecting subfamily of it contains a common element. In this paper we examine the families of vertex neighborhoods of a graph, with the aim of determining whether or not they are Helly, and also whether or nor they are hereditary Helly, that is, each of the induced subgraphs of the graph isHelly.We examine the caseswhere the neighborhoods are all open, or all closed, or mixed… CONTINUE READING