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72
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COMBINATORICS
2006
14 years 9 months ago
2006
Let G be a graph. A vertex labeling of G is distinguishing if the only label-preserving automorphism of G is the identity map. The distinguishing number of G, D(G), is the minimum...
72
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COMBINATORICS
2006
14 years 9 months ago
2006
We prove that n+h 4 vertex guards are always sufficient to see the entire interior of an n-vertex orthogonal polygon P with an arbitrary number h of holes provided that there exis...
108
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COMBINATORICS
2006
14 years 9 months ago
2006
We present an algorithm for finding a system of recurrence relations for the number of permutations of length n that satisfy a certain set of conditions. A rewriting of these rela...
COMBINATORICS
2006
14 years 9 months ago
2006
We prove that the minimum number of distinct hamiltonian paths in a strong tournament of order n is 5 n-1 3 . A known construction shows this number is best possible when n 1 mod...
55
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COMBINATORICS
2006
14 years 9 months ago
2006
We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compos...