Abstract
In this paper we propose a constructive algorithm using constraint propagation to generate 4-critical graph units (4-CGUs) which have only one triangle as subgraph. Based on these units we construct 4-critical graphs using Hajós’ join construction. By choosing Grotztsch graph as the initial graph and carefully selecting the edge to be joined, we make sure that the generated graphs are 4-critical and triangle-free. Experiments show that these graphs are exceptionally hard for backtracking algorithms adopting Brélaz’s heuristics. We also give some preliminary analysis on the source of hardness.
Supported in part by the National Science Foundation of China (grant No. 60125207).
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Liu, S., Zhang, J. (2006). Using Hajós’ Construction to Generate Hard Graph 3-Colorability Instances. In: Calmet, J., Ida, T., Wang, D. (eds) Artificial Intelligence and Symbolic Computation. AISC 2006. Lecture Notes in Computer Science(), vol 4120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11856290_19
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DOI: https://doi.org/10.1007/11856290_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-39728-1
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