TY - JOUR
T1 - A note on even cycles and quasirandom tournaments
AU - Kalyanasundaram, Subrahmanyam
AU - Shapira, Asaf
PY - 2013/7
Y1 - 2013/7
N2 - A cycle C={v1,v2,.,v1} in a tournament T is said to be even, if when walking along C, an even number of edges point in the wrong direction, that is, they are directed from vi+1 to vi. In this short article, we show that for every fixed even integer k≥4, if close to half of the k-cycles in a tournament T are even, then T must be quasirandom.This resolves an open question raised in 1991 by Chung and Graham 1991.
AB - A cycle C={v1,v2,.,v1} in a tournament T is said to be even, if when walking along C, an even number of edges point in the wrong direction, that is, they are directed from vi+1 to vi. In this short article, we show that for every fixed even integer k≥4, if close to half of the k-cycles in a tournament T are even, then T must be quasirandom.This resolves an open question raised in 1991 by Chung and Graham 1991.
KW - eigenvalues
KW - quasirandomness
KW - tournament
UR - http://www.scopus.com/inward/record.url?scp=84877729747&partnerID=8YFLogxK
U2 - 10.1002/jgt.21671
DO - 10.1002/jgt.21671
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AN - SCOPUS:84877729747
SN - 0364-9024
VL - 73
SP - 260
EP - 266
JO - Journal of Graph Theory
JF - Journal of Graph Theory
IS - 3
ER -