Geodesic
A Limit Conjecture on the Number of Hamiltonian Cycles on Thin Triangular Grid Cylinder Graphs
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 405-427

Voir la notice de l'article provenant de la source Library of Science

We continue our research in the enumeration of Hamiltonian cycles (HCs) on thin cylinder grid graphs Cm × Pn+1 by studying a triangular variant of the problem. There are two types of HCs, distinguished by whether they wrap around the cylinder. Using two characterizations of these HCs, we prove that, for fixed m, the number of HCs of both types satisfy some linear recurrence relations. For small m, computational results reveal that the two numbers are asymptotically the same. We conjecture that this is true for all m ≥ 2.
Keywords: contractible Hamiltonian cycles, generating functions, thin triangular grid cylinder graph 
@article{DMGT_2018_38_2_a5,
     author = {Bodro\v{z}a-Panti\'c, Olga and Kwong, Harris and Doroslova\v{c}ki, Rade and Panti\'c, Milan},
     title = {A {Limit} {Conjecture} on the {Number} of {Hamiltonian} {Cycles} on {Thin} {Triangular} {Grid} {Cylinder} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {405--427},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a5/}
}
TY  - JOUR
AU  - Bodroža-Pantić, Olga
AU  - Kwong, Harris
AU  - Doroslovački, Rade
AU  - Pantić, Milan
TI  - A Limit Conjecture on the Number of Hamiltonian Cycles on Thin Triangular Grid Cylinder Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2018
SP  - 405
EP  - 427
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a5/
LA  - en
ID  - DMGT_2018_38_2_a5
ER  - 
%0 Journal Article
%A Bodroža-Pantić, Olga
%A Kwong, Harris
%A Doroslovački, Rade
%A Pantić, Milan
%T A Limit Conjecture on the Number of Hamiltonian Cycles on Thin Triangular Grid Cylinder Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2018
%P 405-427
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a5/
%G en
%F DMGT_2018_38_2_a5
Bodroža-Pantić, Olga; Kwong, Harris; Doroslovački, Rade; Pantić, Milan. A Limit Conjecture on the Number of Hamiltonian Cycles on Thin Triangular Grid Cylinder Graphs. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 2, pp. 405-427. http://geodesic.mathdoc.fr/item/DMGT_2018_38_2_a5/