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Squaring a tournament: A proof of Dean's conjecture
Author(s) -
Fisher David C.
Publication year - 1996
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199609)23:1<43::aid-jgt4>3.0.co;2-k
Subject(s) - tournament , conjecture , digraph , combinatorics , mathematics , square (algebra) , discrete mathematics , geometry
Let the square of a tournament be the digraph on the same nodes with arcs where the directed distance in the tournament is at most two. This paper verifies Dean's conjecture: any tournament has a node whose outdegree is at least doubled in its square. © 1996 John Wiley & Sons, Inc.