Abstract
A module of a graph is a non-empty subset of vertices such that every non-module vertex is either connected to all or none of the module vertices. An indecomposable graph contains no non-trivial module (modules of cardinality 1 and |V| are trivial). We present an algorithm to compute indecomposability preserving elimination sequence, which is faster by a factor of |V| compared to the algorithms based on earlier published work. The algorithm is based on a constructive proof of Ille’s theorem [9]. The proof uses the properties of X-critical graphs, a generalization of critical indecomposable graphs.
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Dubey, C.K., Mehta, S.K. (2006). On Indecomposability Preserving Elimination Sequences. In: Chen, D.Z., Lee, D.T. (eds) Computing and Combinatorics. COCOON 2006. Lecture Notes in Computer Science, vol 4112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11809678_7
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DOI: https://doi.org/10.1007/11809678_7
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