Finding a δ-regular supergraph of minimum order

Authors:
Hans L. Bodlaender;Richard B. Tan;Jan van Leeuwen
Affiliations:
Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH Utrecht, Netherlands;Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH Utrecht, Netherlands and Department of Computer Science, University of Sciences & Arts of Oklahoma, Chick ...;Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH Utrecht, Netherlands
Venue:
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Year:
2003

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Abstract

Akiyama et al. (Elem. Math. 83 (1983) 15) proved that every graph of maximum degree Δ is a subgraph of a Δ-regular graph that has at most Δ + 2 additional vertices. We show that, given a graph of maximum degree Δ, a Δ-regular supergraph of it of minimum order can be computed in O(min {Δ1.5|V|2.5, Δ6 + Δ|V|}) time.