We consider standard algorithms of finite graph theory, like for instance shortest path algorithms. We present two general methods to polynomially extend these algorithms to infi...
We prove that for any fixed r 2, the tree-width of graphs not containing Kr as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of the...
Fedor V. Fomin, Sang-il Oum, Dimitrios M. Thilikos
We introduce a novel technique for drawing proximity graphs in polynomial area and volume. Previously known algorithms produce representations whose size increases exponentially w...
We present a unified framework for designing polynomial time approximation schemes (PTASs) for “dense” instances of many NP-hard optimization problems, including maximum cut,...
This note presents two results on real zeros of chromatic polynomials. The first result states that if G is a graph containing a q-tree as a spanning subgraph, then the chromatic ...