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106
Voted
DAM
1998
15 years 24 days ago
1998
We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the followi...
130
Voted
CORR
2011
Springer
14 years 4 months ago
2011
Springer
Given a graph G = (V, E) and a positive integer k, the Proper Interval Completion problem asks whether there exists a set F of at most k pairs of (V × V ) \ E such that the graph...
100
Voted
COMBINATORICA
2007
15 years 21 days ago
2007
A complete partition of a graph G is a partition of its vertex set in which any two distinct classes are connected by an edge. Let cp(G) denote the maximum number of classes in a ...
130
Voted
JCT
2010
14 years 11 months ago
2010
Let m1, m2, . . . , mt be a list of integers. It is shown that there exists an integer N such that for all n ≥ N, the complete graph of order n can be decomposed into edge-disjo...
90
Voted
SIAMDM
2010
14 years 7 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...