Subdivisions in Digraphs of Large Out-Degree or Large Dichromatic Number
- Pierre Aboulker, Nathann Cohen, F. Havet, W. Lochet, Phablo F. S. Moura, St'ephan Thomass'e
- MathematicsElectronic Journal of Combinatorics
- 4 October 2016
If $D$ is an oriented path, or an in-arborescence, or the union of two directed paths from x to y and a directed path from y tox, then every digraph with minimum out-degree large enough contains a subdivision of $D$.
Detours in Directed Graphs
- F. Fomin, P. Golovach, W. Lochet, Danil Sagunov, Kirill Simonov, Saket Saurabh
- MathematicsSymposium on Theoretical Aspects of Computer…
- 10 January 2022
A new approach to the classical Longest Path problem is proposed, which yields a significantly faster FPT algorithm on undirected graphs and a 2O(k) · nO(1) time algorithm for the problem on directed planar graphs.
Subdivisions of oriented cycles in digraphs with large chromatic number
- Nathann Cohen, F. Havet, W. Lochet, N. Nisse
- MathematicsJournal of Graph Theory
- 25 May 2016
It is shown that for any oriented cycle C, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number and for any cycle with two blocks, every strongly connected digraph with sufficiently large Chromatic number contains a subdivision of C.
A Polynomial Time Algorithm for the k-Disjoint Shortest Paths Problem
- W. Lochet
- Mathematics, Computer ScienceACM-SIAM Symposium on Discrete Algorithms
- 1 January 2021
This paper shows that for any fixed k, the disjoint shortest paths problem admits a polynomial time algorithm and can be extended to treat the case where each path connecting the pair has length at most d(s, t) + C.
A proof of the Erdős-Sands-Sauer-Woodrow conjecture
- N. Bousquet, W. Lochet, Stéphan Thomassé
- MathematicsJournal of combinatorial theory. Series B (Print)
- 23 March 2017
How to Find a Good Explanation for Clustering?
- Sayan Bandyapadhyay, F. Fomin, P. Golovach, W. Lochet, Nidhi Purohit, Kirill Simonov
- Computer ScienceAAAI Conference on Artificial Intelligence
- 13 December 2021
A new model of explainable clustering, inspired by the notion of outliers in robust statistics, is introduced, seeking a small number of points whose removal makes the existing clustering well-explainable.
The shortest disjoint paths problem
- W. Lochet
- MathematicsArXiv
- 22 December 2019
For any fixed k, the existence of a polynomial-time algorithm deciding if, given a graph G and a set of pairs of vertices, there exist vertex-disjoint paths from s_i to t_i such that each of these paths is a shortest path is shown.
Immersion of transitive tournaments in digraphs with large minimum outdegree
- W. Lochet
- MathematicsJournal of combinatorial theory. Series B (Print)
- 31 October 2017
Progress on the adjacent vertex distinguishing edge colouring conjecture
It is shown 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, and that this bound can be reduced to $Delta + 19$.
A Polynomial Kernel for Paw-Free Editing
- E. Eiben, W. Lochet, Saket Saurabh
- MathematicsInternational Symposium on Parameterized and…
- 9 November 2019
The question of compressibility for one of the last two unresolved graphs H on $4$ vertices is positively answered and the first polynomial kernel for paw-free editing with $O(k^{6})$vertices is given.
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