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JCT
2010
14 years 8 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...
JCT
1998
14 years 9 months 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...
JCT
1998
14 years 9 months 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)...
JCT
2007
14 years 9 months 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...
JCT
2007
14 years 9 months 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...