Abstract

It is well known that chordal graphs are exactly the graphs of acyclic simplicial complexes. In this note we consider the analogous class of graphs associated with acyclic cubical complexes. These graphs can be characterized among median graphs by forbidden convex subgraphs. They possess a number of properties (in analogy to chordal graphs) not shared by all median graphs. In particular, we disprove a conjecture of Mulder on star contraction of median graphs. A restricted class of cubical complexes for which this conjecture would hold true is related to perfect graphs.

Full Text
Paper version not known

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.