A good characterization of squares of strongly chordal split graphs

Authors:
Van Bang Le;Ngoc Tuy Nguyen
Affiliations:
Universität Rostock, Institut für Informatik, D-18051 Rostock, Germany;Faculty of Information Technology, Hong Duc University, Thanh Hoa, Viet Nam
Venue:
Information Processing Letters
Year:
2011

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Abstract

The square H^2 of a graph H is obtained from H by adding new edges between every two vertices having distance two in H. Lau and Corneil [Recognizing powers of proper interval, split and chordal graphs, SIAM J. Discrete Math. 18 (2004) 83-102] proved that recognizing squares of split graphs is an NP-complete problem. In contrast, we show that squares of strongly chordal split graphs can be recognized in quadratic-time by giving a structural characterization of these graph class.