Bounding the size of the median graph

Abstract

Median graphs have been presented as an useful tool for capturing the essential information of a set of graphs. The computation of the median graph is a complex task. Exact algorithms are, in the worst case, exponential both in the number of graphs and their size. The known bounds for the minimum and maximum number of nodes of the candidate median graphs are in general very coarse and they can be used to achieve only limited improvements in such algorithms. In this paper we present more accurate bounds based on the well-known concepts of maximum common subgraph and minimum common supergraph. These new bounds on the number of nodes can be used to improve the existing algorithms in the computation of the median graph1. © Springer-Verlag Berlin Heidelberg 2007.