DAM
2011
13 years 7 months ago
2011
An edge-labeling λ for a directed graph G has a weak sense of direction (WSD) if there is a function f that satisfies the condition that for any node u and for any two label seq...
JCT
2010
13 years 11 months ago
2010
The vertex Folkman number F(r, n, m), n < m, is the smallest integer t such that there exists a Km-free graph of order t with the property that every r-coloring of its vertices...
DAM
2000
14 years 8 days ago
2000
The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering e1;:::;er in such a way that for every i = 1;:::...
ENDM
2007
14 years 12 days ago
2007
For the unbiased Maker-Breaker game, played on the hypergraph H, let τM (H) be the smallest integer t such that Maker can win the game within t moves (if the game is a Breaker’...
DM
2007
14 years 12 days ago
2007
: For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G...
CORR
2007
Springer
14 years 13 days ago
2007
Springer
A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest...
EJC
2006
14 years 14 days ago
2006
1 The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices2 either G contains G1 or G contains G2, where G denotes the complement of G. In this...
ENDM
2008
14 years 16 days ago
2008
In this note we report on our recent work, still in progress, regarding Folkman numbers. Let f(2, 3, 4) denote the smallest integer n such that there exists a K4
APPROX
2004
Springer
14 years 5 months ago
2004
Springer
Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1...
STOC
2004
ACM
15 years 22 days ago
2004
ACM
Given d (0, ) let kd be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n, d/n) is either kd or kd + 1 almost surely.