Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Frank Mousset"'
Publikováno v:
Random Structures & Algorithms, 60 (4)
Let $k \geq 2$ be an integer. Kouider and Lonc proved that the vertex set of every graph $G$ with $n \geq n_0(k)$ vertices and minimum degree at least $n/k$ can be covered by $k - 1$ cycles. Our main result states that for every $\alpha > 0$ and $p =
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::66c290bf5888e06d23ba9dd7f6d764f7
https://doi.org/10.1002/rsa.21045
https://doi.org/10.1002/rsa.21045
Publikováno v:
Israel Journal of Mathematics. 235:63-77
The minrank of a graph G on the set of vertices [n] over a field $$\mathbb{F}$$ is the minimum possible rank of a matrix $$M \in \mathbb{F}^{{n}\times{n}}$$ with nonzero diagonal entries such that Mi,j = 0 whenever i and j are distinct nonadjacent ve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3a78a41f36dcab87f8e885fd2abce822
https://doi.org/10.1007/s11856-019-1945-8
https://doi.org/10.1007/s11856-019-1945-8
Publikováno v:
Israel Journal of Mathematics. 234:677-690
Let k and l be positive integers. We prove that if 1 ≤ l ≤ Ok(k6/5), then in every large enough graph G, the fraction of k-vertex subsets that induce exactly l edges is at most 1/e + ok(1). Together with a recent result of Kwan, Sudakov and Tran,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8317b38e088e57ed31ee3aecf924f709
https://doi.org/10.1007/s11856-019-1929-8
https://doi.org/10.1007/s11856-019-1929-8
Publikováno v:
Ann. Probab. 48, no. 1 (2020), 493-525
Given a hypergraph $\Gamma=(\Omega,\mathcal{X})$ and a sequence $\mathbf{p} = (p_\omega)_{\omega\in \Omega}$ of values in $(0,1)$, let $\Omega_{\mathbf{p}}$ be the random subset of $\Omega$ obtained by keeping every vertex $\omega$ independently with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0f841bb60a1e4376698e89608aa1112e
https://doi.org/10.1214/19-aop1371
https://doi.org/10.1214/19-aop1371
Publikováno v:
Random Structures & Algorithms. 53:667-691
A classic result of Erdős, Gyarfas and Pyber states that for every coloring of the edges of $K_n$ with $r$ colors, there is a cover of its vertex set by at most $f(r) = O(r^2 \log r)$ vertex-disjoint monochromatic cycles. In particular, the minimum
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c2a00e3fbe3d19c80080050afcda71d3
https://doi.org/10.1002/rsa.20819
https://doi.org/10.1002/rsa.20819
Publikováno v:
Journal of Combinatorial Theory. Series B, 125
A classic result of Erdős and Posa states that any graph either contains k vertex-disjoint cycles or can be made acyclic by deleting at most O ( k log k ) vertices. Birmele, Bondy, and Reed (2007) raised the following more general question: give
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::afbc48b1d34e73330f7ac84bde9cf304
https://doi.org/10.1016/j.jctb.2017.01.004
https://doi.org/10.1016/j.jctb.2017.01.004
Publikováno v:
Israel Journal of Mathematics. 219:959-982
Let $$\mathcal{G}$$ be a separable family of graphs. Then for all positive constants ϵ and Δ and for every sufficiently large integer n, every sequence G 1,..., G t ∈ $$\mathcal{G}$$ of graphs of order n and maximum degree at most Δ such that $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::64e7a8b3215ba20dd4805facca06be17
https://doi.org/10.1007/s11856-017-1504-0
https://doi.org/10.1007/s11856-017-1504-0
Publikováno v:
The Electronic Journal of Combinatorics. 24
In 1990 Erdős, Faudree, Rousseau and Schelp proved that for $k \ge 2$, every graph with $n \ge k+1$ vertices and $(k-1)(n-k+2)+\binom{k-2}{2}+1$ edges contains a subgraph of minimum degree $k$ on at most $n-\sqrt{n/6k^3}$ vertices. They conjectured
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef77ff6d8c7a2def6de0dd668364fffc
https://doi.org/10.37236/7167
https://doi.org/10.37236/7167
Publikováno v:
SIAM Journal on Discrete Mathematics. 28:1980-1986
In 1976 Erdos, Kleitman, and Rothschild determined asymptotically the logarithm of the number of graphs without a clique of a fixed size $\ell$. In this note we extend their result to the case of forbidden cliques of increasing size. More precisely w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e9fadb92db247ccbf63de1a5cd0c27e
https://doi.org/10.1137/130947878
https://doi.org/10.1137/130947878
Autor:
Frank Mousset, Konstantinos Panagiotou, Johannes Lengler, Angelika Steger, Hafsteinn Einarsson
Publikováno v:
Ann. Appl. Probab. 26, no. 5 (2016), 3206-3250
In an Achlioptas process, starting with a graph that has n vertices and no edge, in each round $d \geq 1$ edges are drawn uniformly at random, and using some rule exactly one of them is chosen and added to the evolving graph. For the class of Achliop
Externí odkaz:
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http://projecteuclid.org/euclid.aoap/1476884316
http://projecteuclid.org/euclid.aoap/1476884316
