Zobrazeno 1 - 10
of 82
pro vyhledávání: '"Cecil C. Rousseau"'
Publikováno v:
Journal of Graph Theory. 86:286-294
Autor:
Vladimir Nikiforov, Cecil C. Rousseau
Publikováno v:
Random Structures and Algorithms. 27:379-400
A book Bp is a graph consisting of p triangles sharing a common edge. In this paper we prove that if p ≤ q/6 - o(q) and q is large, then the Ramsey number r (Bp, Bq) is given by r(Bp, Bq) = 2q + 3, and the constant 1/6 is essentially best possible.
Autor:
Vladimir Nikiforov, Cecil C. Rousseau
Publikováno v:
Journal of Graph Theory. 49:168-176
Autor:
Cecil C. Rousseau, Vladimir Nikiforov
Publikováno v:
Journal of Combinatorial Theory, Series B. 92:85-97
Let B q (r) = K r + qK 1 be the graph consisting of q distinct (r + 1)-cliques sharing a common r-clique. We prove that if p ≥ 2 and r ≥ 3 are fixed, then r(K p+1 ,B q (r))=p(q + r - 1) + 1 for all sufficiently large q.
Autor:
Cecil C. Rousseau, S. E. Speed
Publikováno v:
Combinatorics, Probability and Computing. 12:653-660
Given a graph Hwith no isolates, the (generalized) mixed Ramsey number is the smallest integer r such that every H-free graph of order r contains an m-element irredundant set. We consider some questions concerning the asymptotic behaviour of this num
Publikováno v:
Journal of Computational and Applied Mathematics. 142:107-114
Wilf posed the following problem: determine asymptotically as $n\to\infty$ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem was given by Hitczenko and Savage. In t
Publikováno v:
Discrete Mathematics. 248:249-254
Given a monotone graphical property Q, how large should d(n) be to ensure that if (Hn) is any sequence of graphs satisfying |Hn|=n and δ(Hn)⩾d(n), then almost every induced subgraph of Hn has property Q? We prove essentially best possible results
Publikováno v:
Graphs and Combinatorics. 17:123-128
We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nf a +1(d), where f a +1(d)=∫0 1(((1−t)1/( a +1))/(a+1+(d−
Autor:
Cecil C. Rousseau, Steven R. Dunbar
Publikováno v:
Mathematics Magazine. 83:156-158
(2010). 38th United States of America Mathematical Olympiad. Mathematics Magazine: Vol. 83, No. 2, pp. 156-158.
Publikováno v:
Discrete Mathematics. 220:51-56
The Ramsey number r(H,Kn) is the smallest integer N so that each graph on N vertices that fails to contain H as a subgraph has independence number at least n. It is shown that r(K 2,m ,K n )⩽(m−1+ o (1))(n/ log n) 2 and r(C 2m ,K n )⩽c(n/ log n