A Note on Contractible Edges in Chordal Graphs

Details A Note on Contractible Edges in Chordal Graphs A Note on Contractible Edges in Chordal Graphs

2009-02-09

arxiv.org/abs/0902.1364v1

Computer Science

Discrete Mathematics

Scientific paper

Contraction of an edge merges its end points into a new vertex which is adjacent to each neighbor of the end points of the edge. An edge in a $k$-connected graph is {\em contractible} if its contraction does not result in a graph of lower connectivity. We characterize contractible edges in chordal graphs using properties of tree decompositions with respect to minimal vertex separators.

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