A fast practical algorithm for the vertex separation of unicyclic graphs

Date

2008-04-10T06:01:02Z

Authors

Markov, Minko Marinov.

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Abstract

The vertex separation of a graph is the minimum vertex separation of a linear layout of that graph over all its linear layouts. A linear layout of a graph is an arrangement of its vertices in a line and the vertex separation of a linear layout is maximum number of vertices to the left of any intervertex "gap" that are adjacent to vertices to the right of that gap, over all gaps. A unicyclic graph is a connected graph with precisely one cycle that is, a tree plus an extra edge. We present a O(n lgn) algorithm to compute the optimal vertex separation of unicyclic graphs. The algorithm is "practical" in the sense that it is easily implementable. Furthermore, the algorithm outputs a layout for the unicyclic graph of minimum vertex separation.

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