On strong Menger-connectivity of star graphs

Authors:
Eunseuk Oh;Jianer Chen
Affiliations:
Department of Computer Science, Texas A&M University, College Station, TX;Department of Computer Science, Texas A&M University, College Station, TX
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

Motivated by parallel routing in networks with faults, we study the following graph theoretical problem. Let G be a graph of minimum vertex degree d. We say that G is strongly Menger-connected if for any copy Gf of G with at most d - 2 nodes removed, every pair of nodes u and v in Gf are connected by min{degf(u), degf(v)} node-disjoint paths in Gf, where degf(u) and degf(v) are the degrees of the nodes u and v in Gf, respectively. We show that the star graphs, which are a recently proposed attractive alternative to the widely used hypercubes as network models, are strongly Menger-connected. An algorithm of optimal running time is developed that constructs the maximum number of node-disjoint paths of nearly optimal length in star graphs with faults.