TY - JOUR
T1 - [a,b]-factors of graphs on surfaces
AU - Matsubara, Ryota
AU - Matsuda, Haruhide
AU - Matsuo, Nana
AU - Noguchi, Kenta
AU - Ozeki, Kenta
N1 - Funding Information:
This work was supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research(C), Grant Number 15K04980.This work was supported by JSPS KAKENHI, Grant-in-Aid for Young Scientists(B), Grant Number 17K14239.This work was supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research(C), Grant Number 18K03391.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/7
Y1 - 2019/7
N2 - A well-known conjecture of Grünbaum (1970) and Nash-Williams (1971) asserts that every 4-connected toroidal graph has a Hamiltonian cycle. Related to this conjecture, Kawarabayashi and Ozeki (2011) proved two results on a 2-factor and a 3-factor. In this paper, motivated by these results, we give several sufficient conditions for a graph embedded in a surface to have an [a,b]-factor. We also show that several conditions are best possible.
AB - A well-known conjecture of Grünbaum (1970) and Nash-Williams (1971) asserts that every 4-connected toroidal graph has a Hamiltonian cycle. Related to this conjecture, Kawarabayashi and Ozeki (2011) proved two results on a 2-factor and a 3-factor. In this paper, motivated by these results, we give several sufficient conditions for a graph embedded in a surface to have an [a,b]-factor. We also show that several conditions are best possible.
KW - Factor
KW - Graph
KW - Hamiltonian cycle
KW - Surface
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U2 - 10.1016/j.disc.2019.03.016
DO - 10.1016/j.disc.2019.03.016
M3 - Article
AN - SCOPUS:85064274539
SN - 0012-365X
VL - 342
SP - 1979
EP - 1988
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 7
ER -