Convex excess in partial cubes
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Colleges, School and Institutes
The convex excess ce(G) of a graph G is introduced as inline image where the summation goes over all convex cycles of G. It is proved that for a partial cube G with n vertices, m edges, and isometric dimension i(G), inequality 2n−m−i(G)−ce(G)≤2 holds. Moreover, the equality holds if and only if the so-called zone graphs of G are trees. This answers the question from Bre inline image r et al. [Tiled partial cubes, J Graph Theory 40 (2002) 91–103] whether partial cubes admit this kind of inequalities. It is also shown that a suggested inequality from Bre inline image r et al. [Tiled partial cubes, J Graph Theory 40 (2002) 91–103] does not hold. Copyright © 2011 John Wiley & Sons, Ltd.
|Number of pages||14|
|Journal||Journal of Graph Theory|
|Early online date||3 Mar 2011|
|Publication status||Published - 1 Apr 2012|