Characterizing Intersection Graphs of Substars of a Star

Marcia R.Cerioli1, Jayme L.Szwarcfiter2
1Universidade Federal do Rio de Janeiro, Instituto de Matemdtica and COPPE, Caixa Postal 68530, 21945-970, Rio de Janeiro, RJ, Brasil,
2Universidade Federal do Rio de Janeiro, Instituto de Matematica, Nticleo de Com- putac#o Eletrénica and COPPE, Caixa Postal 2324, 2001-970, Rio de Janeiro, RJ, Brasil.

Abstract

Starlike graphs are the intersection graphs of substars of a star. We describe different characterizations of starlike graphs, including one by forbidden subgraphs. In addition, we present characterizations for a natural subclass of it, the starlike-threshold graphs.