Abstract
In this paper, we consider the recognition problem on a class of perfectly orderable graphs, namely, the HHD-free graphs, i.e., graphs that do not contain any induced subgraph isomorphic to a house, a hole, or a domino. We prove properties of the HHD-free graphs which enable us to present an O(n m)-time and O(n + m)-space algorithm for determining whether a given graph G on n vertices and m edges is HHD-free. The algorithm can be augmented to provide a certificate (an induced house, hole, or domino) whenever it decides that the input graph is not HHD-free; the certificate computation requires O(n + m) additional time and O(n) space.
This research was co-funded by the European Union in the framework of the program “Pythagoras II” of the “Operational Program for Education and Initial Vocational Training” of the 3rd Community Support Framework of the Hellenic Ministry of Education, funded by national sources and the European Social Fund (ESF).
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Nikolopoulos, S.D., Palios, L. (2007). An O(nm)-Time Certifying Algorithm for Recognizing HHD-Free Graphs. In: Preparata, F.P., Fang, Q. (eds) Frontiers in Algorithmics. FAW 2007. Lecture Notes in Computer Science, vol 4613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73814-5_27
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DOI: https://doi.org/10.1007/978-3-540-73814-5_27
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