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104
Voted
JCT
2010
14 years 11 months ago
2010
Abstract. A weighting of the edges of a graph is called vertexcoloring if the weighted degrees of the vertices yield a proper coloring of the graph. In this paper we show that such...
98
Voted
JCT
1998
15 years 11 days ago
1998
The aim of this note is to point out some combinatorial applications of a lemma of Scarf, proved first in the context of game theory. The usefulness of the lemma in combinatorics...
114
Voted
JCT
1998
15 years 11 days ago
1998
Let Q(N) denote the number of partitions of N into distinct parts. If ω(k) := 3k2 +k 2 , then it is well known that Q(N) + ∞X k=1 (−1)k “ Q(N − 2ω(k)) + Q(N − 2ω(−k)...
100
Voted
JCT
2007
15 years 18 days ago
2007
A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. The importance of bricks stems from the fact that...
113
Voted
JCT
2007
15 years 6 days ago
2007
A k-triangulation of a convex polygon is a maximal set of diagonals so that no k + 1 of them mutually cross in their interiors. We present a bijection between 2-triangulations of a...