Characterization of irreducible Boolean matrices with the largest generalized competition index

Kim, Hwa Kyung

doi:10.1016/j.laa.2014.10.004

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Cited by 6 publications

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“…Such an integer p is called the competition period of D and is denoted by cperiod(D). Refer to [15,16,17] for some results of competition indices and competition periods of digraphs.…”

Section: Introductionmentioning

confidence: 99%

On competition indices and periods of multipartite tournaments

Jung,

Kim,

Yoon

2020

Preprint

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In this paper, we compute competition indices and periods of multipartite tournaments. We first show that the competition period of an acyclic digraph D is one and ζ(D) + 1 is a sharp upper bound of the competition index of D where ζ(D) is the sink elimination index of D. Then we prove that, especially, for an acyclic k-partite tournament D, the competition index of D is ζ(D) or ζ(D) + 1 for an integer k ≥ 3. By developing useful tools to create infinitely many directed walks in a certain regular pattern from given directed walks, we show that the competition period of a multipartite tournament with sinks and directed cycles is at most three. We also prove that the competition index of a primitive digraph does not exceed its exponent.

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“…Such an integer p is called the competition period of D and is denoted by cperiod(D). Refer to [15,16,17] for some results of competition indices and competition periods of digraphs.…”

Section: Introductionmentioning

confidence: 99%