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SIAMDM
2010
13 years 2 months ago
2010
The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In t...
DM
2008
13 years 8 months ago
2008
A set S of vertices of a graph G is a geodetic set if every vertex of G lies in at least one interval between the vertices of S. The size of a minimum geodetic set in G is the geo...
ENDM
2008
13 years 8 months ago
2008
A strong oriented k-coloring of an oriented graph G is a homomorphism from G to H having k vertices labelled by the k elements of an abelian additive group M, such that for any p...
DAM
2007
13 years 7 months ago
2007
The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees...
STOC
2004
ACM
14 years 8 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.