Replacing cliques by stars in quasi-median graphs
2004 (English)In: Discrete Applied Mathematics, Vol. 143, no 1-3, 194-203 p.Article in journal (Refereed) Published
For a multi-set Sigma of splits (bipartitions) of a finite set X, we introduce the multi-split graph G(Sigma). This graph is a natural extension of the Buneman graph. Indeed, it is shown that several results pertaining to the Buneman graph extend to the multi-split graph. In addition, in case Sigma is derived from a set R of partitions of X by taking parts together with their complements, we show that the extremal instances where R is either strongly compatible or strongly incompatible are equivalent to G(Sigma) being either a tree or a Cartesian product of star trees, respectively.
Place, publisher, year, edition, pages
2004. Vol. 143, no 1-3, 194-203 p.
split, (in)compatibility, strong (in)compatibility. buneman graph, multi-split graph, quasi-median graph, networks, trees
IdentifiersURN: urn:nbn:se:uu:diva-71813OAI: oai:DiVA.org:uu-71813DiVA: diva2:99724