Deleting vertices to graphs of bounded genus [article]

Tomasz Kociumaka, Marcin Pilipczuk
2017 arXiv   pre-print
We show that a problem of deleting a minimum number of vertices from a graph to obtain a graph embeddable on a surface of a given Euler genus is solvable in time 2^C_g · k^2 k n^O(1), where k is the size of the deletion set, C_g is a constant depending on the Euler genus g of the target surface, and n is the size of the input graph. On the way to this result, we develop an algorithm solving the problem in question in time 2^O((t+g) (t+g)) n, given a tree decomposition of the input graph of
more » ... t. The results generalize previous algorithms for the surface being a sphere by Marx and Schlotter [Algorithmica 2012], Kawarabayashi [FOCS 2009], and Jansen, Lokshtanov, and Saurabh [SODA 2014].
arXiv:1706.04065v1 fatcat:5fdhoa3aejfbnnjrq3ugklvxze