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Existence of openly disjoint circuits through a vertex
Author(s) -
Mader W.
Publication year - 2010
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/jgt.20411
Subject(s) - digraph , combinatorics , disjoint sets , pairwise comparison , mathematics , vertex (graph theory) , discrete mathematics , graph , electronic circuit , physics , statistics , quantum mechanics
We deal with conditions for a digraph of minimum degree r which imply the existence of a vertex x contained in r circuits which have pairwise only x in common. In particular, we give some positive answers to a question of P. Seymour, whether an r ‐regular digraph has a vertex x which is contained in r circuits pairwise disjoint except for x , and show that the answer, in general, is negative. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 93–105, 2010