Disjoint circuits in the cartesian product of two directed cycles | Zendy

Curran Stephen | Zendy

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Disjoint circuits in the cartesian product of two directed cycles

Author(s) -

Curran Stephen

Publication year - 1994

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.3190180213

Subject(s) - cartesian product , mathematics , digraph , combinatorics , knot (papermaking) , disjoint sets , cayley graph , abelian group , discrete mathematics , graph , chemical engineering , engineering

We show that the Cartesian product of two directed cycles Z a X Z b has r disjointly embedded circuits C 1 , C 2 , ⃛, C r with specified knot classes knot (C i ) = (m i , n i ) , for i = 1, 2, ⃛, r , if and only if there exist relatively prime non‐negative integers m and n such that knot (C i ) = (m, n) , for i = 1, 2, ⃛, r , and r(am + bn) ≦ ab. We generalize this result to the Cayley digraph on a finite abelian group with a two‐element generating set.

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