International Workshop on Experimental and Efficient Algorithms

WEA 2004: Experimental and Efficient Algorithms pp 87-99

# Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P4’s

• Hans L. Bodlaender
• Celina M. H. de Figueiredo
• Marisa Gutierrez
• Ton Kloks
• Rolf Niedermeier
Conference paper

DOI: 10.1007/978-3-540-24838-5_7

Volume 3059 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Bodlaender H.L., de Figueiredo C.M.H., Gutierrez M., Kloks T., Niedermeier R. (2004) Simple Max-Cut for Split-Indifference Graphs and Graphs with Few P4’s. In: Ribeiro C.C., Martins S.L. (eds) Experimental and Efficient Algorithms. WEA 2004. Lecture Notes in Computer Science, vol 3059. Springer, Berlin, Heidelberg

## Abstract

The simple max-cut problem is as follows: given a graph, find a partition of its vertex set into two disjoint sets, such that the number of edges having one endpoint in each set is as large as possible. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The simple max-cut decision problem is known to be NP-complete for split graphs. An indifference graph is the intersection graph of a set of unit intervals of the real line. We show that the simple max-cut problem can be solved in linear time for a graph that is both split and indifference. Moreover, we also show that for each constant q, the simple max-cut problem can be solved in polynomial time for (q,q-4)-graphs. These are graphs for which no set of at most q vertices induces more than q-4 distinct P4’s.

## Authors and Affiliations

• Hans L. Bodlaender
• 1
• Celina M. H. de Figueiredo
• 2
• Marisa Gutierrez
• 3
• Ton Kloks
• 4
• Rolf Niedermeier
• 5
1. 1.Institute of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
2. 2.Instituto de Matemática and COPPEUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
3. 3.Departamento de MatemáticaUniversidad Nacional de La Plata, C. C. 172 (1900)La PlataArgentina
4. 4.
5. 5.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany