Zobrazeno 1 - 10
of 72
pro vyhledávání: '"WATRIGANT, RÉMI"'
In 1949, Zykov proposed the first explicit construction of triangle-free graphs with arbitrarily large chromatic number. We define a Zykov graph as any induced subgraph of a graph created using Zykov's construction. We give a structural characterizat
Externí odkaz:
http://arxiv.org/abs/2410.06917
We revisit the classical problem of channel allocation for Wi-Fi access points (AP). Using mechanisms such as the CSMA/CA protocol, Wi-Fi access points which are in conflict within a same channel are still able to communicate to terminals. In graph t
Externí odkaz:
http://arxiv.org/abs/2408.14633
We prove a number of results related to the computational complexity of recognizing well-covered graphs. Let $k$ and $s$ be positive integers and let $G$ be a graph. Then $G$ is said - $\mathbf{W_k}$ if for any $k$ pairwise disjoint independent verte
Externí odkaz:
http://arxiv.org/abs/2404.07853
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation trade-off
Externí odkaz:
http://arxiv.org/abs/2207.07708
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational complexity o
Externí odkaz:
http://arxiv.org/abs/2204.05809
We study the existence of polynomial kernels, for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. Our main result is that a polynomial kernel for $k$-Dominating Set on graphs of t
Externí odkaz:
http://arxiv.org/abs/2107.02882
We recently introduced the graph invariant twin-width, and showed that first-order model checking can be solved in time $f(d,k)n$ for $n$-vertex graphs given with a witness that the twin-width is at most $d$, called $d$-contraction sequence or $d$-se
Externí odkaz:
http://arxiv.org/abs/2007.14161
The twin-width of a graph $G$ is the minimum integer $d$ such that $G$ has a $d$-contraction sequence, that is, a sequence of $|V(G)|-1$ iterated vertex identifications for which the overall maximum number of red edges incident to a single vertex is
Externí odkaz:
http://arxiv.org/abs/2006.09877
Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA '14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit $d$-dimension
Externí odkaz:
http://arxiv.org/abs/2004.14789
We study the approximability of the Maximum Independent Set (MIS) problem in $H$-free graphs (that is, graphs which do not admit $H$ as an induced subgraph). As one motivation we investigate the following conjecture: for every fixed graph $H$, there
Externí odkaz:
http://arxiv.org/abs/2004.12166