DAM
2011
12 years 11 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 3 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 4 months 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
13 years 10 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
14 years 5 months 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.