eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Open Access Series in Informatics
2190-6807
2019-01-08
14:1
14:9
10.4230/OASIcs.SOSA.2019.14
article
Simple Greedy 2-Approximation Algorithm for the Maximum Genus of a Graph
Kotrbcík, Michal
Skoviera, Martin
The maximum genus gamma_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 describe a greedy 2-approximation algorithm for maximum genus by proving that removing pairs of adjacent edges from G arbitrarily while retaining connectedness leads to at least gamma_M(G)/2 pairs of edges removed. As a consequence of our approach we also obtain a 2-approximate counterpart of Xuong's combinatorial characterisation of maximum genus.
https://drops.dagstuhl.de/storage/01oasics/oasics-vol069-sosa2019/OASIcs.SOSA.2019.14/OASIcs.SOSA.2019.14.pdf
maximum genus
embedding
graph
greedy algorithm