Abstract
An isomorphism certificate of a labeled tournament T is a labeled subdigraph of T which together with an unlabeled copy of T allows the errorless reconstruction of T. It is shown that any tournament on n vertices contains an isomorphism certificate with at most n log2 n edges. This answers a question of Fishburn, Kim and Tetali. A score certificate of T is a labeled subdigraph of T which together with the score sequence of T allows its errorless reconstruction. It is shown that there is an absolute constant ∈ > 0 so that any tournament on n vertices contains a score certificate with at most (1/2 - ∈)n2 edges.
Original language | English |
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Article number | R12 |
Pages (from-to) | 1-6 |
Number of pages | 6 |
Journal | Electronic Journal of Combinatorics |
Volume | 4 |
Issue number | 1 R |
DOIs | |
State | Published - 1997 |