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COMBINATORICS
2007
15 years 3 months ago
2007
Let G = (V, E) be any d-regular graph with girth g on n vertices, for d ≥ 3. This note shows that G has a maximum matching which includes all but an exponentially small fraction...
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COMBINATORICS
2007
15 years 3 months ago
2007
A k-ary necklace of order n is an equivalence class of strings of length n of symbols from {0, 1, . . . , k − 1} under cyclic rotation. In this paper we define an ordering on t...
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COMBINATORICS
2007
15 years 3 months ago
2007
A genus one labeled circle tree is a tree with its vertices on a circle, such that together they can be embedded in a surface of genus one, but not of genus zero. We define an e-...
COMBINATORICS
2007
15 years 3 months ago
2007
This work introduces the technique of using a carefully chosen determining set to prove the existence of a distinguishing labeling using few labels. A graph G is said to be d-dist...
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COMBINATORICS
2007
15 years 3 months ago
2007
We determine the limiting distributions of the longest alternating subsequence for pattern-restricted permutations in which the pattern is any one of the six patterns of length th...