arXiv subjects

Heather Gavlas

Publications and source records attributed to Heather Gavlas.

2 recordsLinked to original sources

arXiv2001

Hamiltonian Paths in Cartesian Powers of Directed Cycles

The vertex set of the kth cartesian power of a directed cycle of length m can be naturally identified with the set of k-tuples of integers modulo m. For any two vertices v and w of this graph, it is easy to see that if there is a hamiltonian path from v to w, then the sum of the coordinates of v is congruent, modulo m, to one more than the sum of the coordinates of w. We prove the converse, unless k = 2 and m is odd.

math.CO↗

arXiv1997

Automorphism groups with cyclic commutator subgroup and Hamilton cycles

It has been shown that there is a Hamilton cycle in every connected Cayley graph on each group G whose commutator subgroup is cyclic of prime-power order. This paper considers connected, vertex-transitive graphs X of order at least 3 where the automorphism group of X contains a transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs, only the Petersen graph is not hamiltonian.

math.CO↗