• Publications
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Subdivisions of oriented cycles in digraphs with large chromatic number
TLDR
An oriented cycle is an orientation of a undirected cycle. Expand
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Subdivisions in Digraphs of Large Out-Degree or Large Dichromatic Number
TLDR
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
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A proof of the Erdős-Sands-Sauer-Woodrow conjecture
TLDR
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
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The shortest disjoint paths problem
  • W. Lochet
  • Mathematics, Computer Science
  • ArXiv
  • 22 December 2019
TLDR
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
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A Polynomial Kernel for Paw-Free Editing
TLDR
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
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Fault Tolerant Subgraphs with Applications in Kernelization
TLDR
In the past decade, the design of fault tolerant data structures for networks has become a central topic of research. Expand
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The directed 2-linkage problem with length constraints
TLDR
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
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A proof of the Erd\H{o}s-Sands-Sauer-Woodrow conjecture
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 byExpand
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Exact and Approximate Digraph Bandwidth
TLDR
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
Progress on the adjacent vertex distinguishing edge colouring conjecture
TLDR
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
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