Simple greedy 2-approximation algorithm for the maximum genus of a graph [article]

Michal Kotrbcik, Martin Skoviera
2015 arXiv   pre-print
The maximum genus γ_M(G) of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal results in a connected spanning subgraph of G. In this paper we prove that removing pairs of adjacent edges from G arbitrarily while retaining connectedness leads to at least γ_M(G)/2 pairs of edges removed. This allows us to describe a greedy algorithm for the
more » ... m genus of a graph; our algorithm returns an integer k such that γ_M(G)/2< k <γ_M(G), providing a simple method to efficiently approximate maximum genus. As a consequence of our approach we obtain a 2-approximate counterpart of Xuong's combinatorial characterisation of maximum genus.
arXiv:1501.07460v1 fatcat:tfabfjp5s5ghnakwtm46w4hqte