On the hyperbolicity constant of circular-arc graphs Articles uri icon

publication date

  • June 2019

start page

  • 244

end page

  • 256

volume

  • 263

International Standard Serial Number (ISSN)

  • 0166-218X

Electronic International Standard Serial Number (EISSN)

  • 1872-6771

abstract

  • Gromov hyperbolicity is an interesting geometric property, and so it is natural to study it in the context of geometric graphs. It measures the tree-likeness of a graph from a metric viewpoint. In particular, we are interested in circular-arc graphs, which is an important class of geometric intersection graphs. In this paper we give sharp bounds for the hyperbolicity constant of (finite and infinite) circular-arc graphs. Moreover, we obtain bounds for the hyperbolicity constant of the complement and line of any circular-arc graph. In order to do that, we obtain new results about regular, chordal and line graphs which are interesting by themselves.

keywords

  • circular graphs; circular-arc graphs<, geometric graphs; gromov hyperbolicity; geodesics