78
Voted
IPL
2007
15 years 11 days ago
2007
For a given connected graph G of order n, a routing R in G is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forw...
96
Voted
SIAMDM
2008
15 years 11 days ago
2008
Let G be a connected graph, and let V and V two n-element subsets of its vertex set V (G). Imagine that we place a chip at each element of V and we want to move them into the posi...
106
Voted
GC
2007
Springer
15 years 12 days ago
2007
Springer
Let G be a connected graph of order n and girth g. If dG(u) + dG(v) ≥ n − 2g + 5 for any two non-adjacent vertices u and v, then G is up-embeddable. Further more, the lower bou...
116
Voted
CORR
2007
Springer
15 years 13 days ago
2007
Springer
For a given connected graph G on n vertices and m edges, we prove that its independence number α(G) is at least ((2m+n+2) -((2m+n+2)2 -16n2 )½ )/8. Keywords : independence numbe...
94
Voted
DM
2008
15 years 16 days ago
2008
In [2], Duffus et al. showed that every connected graph G which contains no induced subgraph isomorphic to a claw or a net is traceable. And they also showed that if a 2-connected...
92
Voted
DM
2008
15 years 16 days ago
2008
Consider a configuration of pebbles distributed on the vertices of a connected graph of order n. A pebbling step consists of removing two pebbles from a given vertex and placing o...
80
Voted
EJC
2010
15 years 16 days ago
2010
Let S be a connected graph which contains an induced path of n-1 vertices, where n is the order of S. We consider a puzzle on S. A configuration of the puzzle is simply an n-dimen...
DAM
2008
15 years 16 days ago
2008
A vertex-cut X is said to be a restricted cut of a graph G if it is a vertex-cut such that no vertex u in G has all its neighbors in X. Clearly, each connected component of G - X ...
72
Voted
DM
2010
15 years 16 days ago
2010
Let G be a connected graph, suppose that v is a vertex of G, and denote the subgraph formed from G by deleting vertex v by G \ v. Denote the algebraic connectivities of G and G \ ...
42
Voted
CORR
2010
Springer
15 years 16 days ago
2010
Springer
We show that for every connected graph G of diameter 3, the graph G3 has average degree 7 4 (G). We also provide an example showing that this bound is best possible. This resolv...