TY - JOUR
T1 - Cubic Neighbourhoods in Triple Systems
AU - Colbourn, Charles J.
AU - McKay, Brendan D.
N1 - Funding Information:
Thanks to Alex Rosa, and to the referee, for helpful comments. also acknowledges the financial support of NSERC Canada.
PY - 1987/1
Y1 - 1987/1
N2 - In a triple system of index 3, the multiset of pairs appearing in triples with a fixed element form a cubic multigraph called the neighbourhood of the element. We prove that, with precisely three exceptions, every cubic multigraph appears as an element neighbourhood in a triple system. The proof technique involves establishing the existence of certain path factorizations of cubic graphs.
AB - In a triple system of index 3, the multiset of pairs appearing in triples with a fixed element form a cubic multigraph called the neighbourhood of the element. We prove that, with precisely three exceptions, every cubic multigraph appears as an element neighbourhood in a triple system. The proof technique involves establishing the existence of certain path factorizations of cubic graphs.
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U2 - 10.1016/S0304-0208(08)72880-9
DO - 10.1016/S0304-0208(08)72880-9
M3 - Article
AN - SCOPUS:77952175795
SN - 0304-0208
VL - 149
SP - 119
EP - 136
JO - North-Holland Mathematics Studies
JF - North-Holland Mathematics Studies
IS - C
ER -