IMASL   20939
INSTITUTO DE MATEMATICA APLICADA DE SAN LUIS "PROF. EZIO MARCHI"
Unidad Ejecutora - UE
artículos
Título:
On the Hamilton-Waterloo problem: the case of two cycles sizes of different parity
Autor/es:
MELISSA KERANEN; ADRIÁN PASTINE
Revista:
Ars Mathematica Contemporanea
Editorial:
University of Primorska
Referencias:
Lugar: Primorska; Año: 2019 vol. 17 p. 525 - 533
ISSN:
1855-3966
Resumen:
The Hamilton-Waterloo problem asks for a decomposition of the complete graph of order v into r copies of a 2-factor F_{1} and s copies of a 2-factor F_{2} such that r+s=leftlfloorrac{v-1}{2}ightfloor. If F_{1} consists of m-cycles and F_{2} consists of n cycles, we say that a solution to (m,n)-HWP(v;r,s) exists. The goal is to find a decomposition for every possible pair (r,s). In this paper, we show that for odd x and y, there is a solution to (2^kx,y)-HWP(vm;r,s) if gcd(x,y)geq 3, mgeq 3, and both x and y divide v, except possibly when 1in {r,s}.