Abstract
We study two different types of graphs that contain even cycles and, possibly, some chords. The objective is to analyze some properties of these types of graphs that can be used to solve perfect matching optimization problems with side constraints. In particular, we obtain the maximum number of edges of certain classes that can occur in the solutions to the considered problems. Finally, we apply the obtained results to derive a class of valid inequalities and a possible enumerative scheme.
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Fernández, E., Meza, O. Even Cycles and Perfect Matching Problems with Side Constraints. Journal of Combinatorial Optimization 8, 381–396 (2004). https://doi.org/10.1023/B:JOCO.0000038916.51082.5e
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DOI: https://doi.org/10.1023/B:JOCO.0000038916.51082.5e