In 1985, Mader conjectured the existence of a function $f$ such that every digraph with minimum out-degree at least $f(k)$ contains a subdivision of the transitive tournament of order $k$.Expand

A very nice result of Barany and Lehel asserts that every finite subset X or R d can be covered by h ( d ) X-boxes (i.e. each box has antipodal points in X).Expand

We show the existence of a polynomial-time algorithm deciding if, given a graph $G$ and a set of pairs of vertices $(s_1, t_1), there exist $k$ vertex-disjoint paths from $s_i$ to $t_i$, such that each of these paths is a shortest path.Expand

For a fixed graph $H$, the $H$-free-editing problem asks whether we can modify a given graph $G$ by adding or deleting at most $k$ edges such that the resulting graph does not contain $H $ as an induced subgraph.Expand

We prove that, unless the exponential time hypothesis (ETH) fails, there is no polynomial algorithm for deciding the existence of a solution $P_1,P_2$ to the weak k-linkage problem which we formulate below for digraphs.Expand

A very nice result of B\'ar\'any and Lehel asserts that every finite subset $X$ or $\mathbb R^d$ can be covered by $f(d)$ $X$-boxes (i.e. each box has two antipodal points in $X$). As shown by… Expand

In this paper, we introduce a directed variant of the classical Bandwidth problem and study it from the view-point of moderately exponential time algorithms, both exactly and approximately.Expand

We show that every graph with maximum degree $\Delta$ and no isolated edge has an adjacent vertex distinguishing edge colouring with $\Delta + 300$ colours, provided $\Delta is large enough.Expand