Abstract

The Burling sequence is a sequence of triangle-free graphs of increasing chromatic number. Each of them is isomorphic to the intersection graph of a set of axis-parallel boxes in R3. These graphs were also proved to have other geometrical representations: intersection graphs of line segments in the plane, and intersection graphs of frames, where a frame is the boundary of an axis-aligned rectangle in the plane.We call Burling graph every graph that is an induced subgraph of some graph in the Burling sequence. We give five new equivalent ways to define Burling graphs. Three of them are geometrical, one is of a more graph-theoretical flavor, and one, that we call abstract Burling graphs, is more axiomatic.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.