A note on maximal hamiltonian cycles in the square of a graph

1988 ◽  
Vol 21 (4) ◽  
pp. 1089-1093
Author(s):  
Tomasz Traczyk
Keyword(s):  
Hamiltonian Cycles ◽  
Square Of A Graph

scholarly journals Induced S(K1,3) and hamiltonian cycles in the square of a graph

1999 ◽  
Vol 207 (1-3) ◽  
pp. 263-269 ◽  
Author(s):  
Mohamed El Kadi Abderrezzak ◽  
Evelyne Flandrin ◽  
Zdeněk Ryjáček
Keyword(s):  
Hamiltonian Cycles ◽  
Square Of A Graph

scholarly journals Hamiltonian Cycles in the Square of a Graph

10.37236/690 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Jan Ekstein
Keyword(s):  
Connected Graph ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Hamiltonian Cycles ◽  
Block Graph ◽  
Cut Vertex ◽  
Necessary And Sufficient ◽  
Square Of A Graph

We show that under certain conditions the square of the graph obtained by identifying a vertex in two graphs with hamiltonian square is also hamiltonian. Using this result, we prove necessary and sufficient conditions for hamiltonicity of the square of a connected graph such that every vertex of degree at least three in a block graph corresponds to a cut vertex and any two these vertices are at distance at least four.

Hamiltonicity of a class of toroidal graphs

2020 ◽  
Vol 70 (2) ◽  
pp. 497-503
Author(s):  
Dipendu Maity ◽  
Ashish Kumar Upadhyay
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycle ◽  
Partial Solution ◽  
The Other ◽  
Hamiltonian Cycles ◽  
The Face ◽  
Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

scholarly journals Hamiltonian Cycles in Strong Products of Graphs

1979 ◽  
Vol 22 (3) ◽  
pp. 305-309 ◽  
Author(s):  
J. C. Bermond ◽  
A. Germa ◽  
M. C. Heydemann
Keyword(s):  
Connected Graph ◽  
Hamiltonian Cycles ◽  
Strong Product

Abstract. Let denote the graph (k times) where is the strong product of the two graphs G and H. In this paper we prove the conjecture of J. Zaks [3]: For every connected graph G with at least two vertices there exists an integer k = k(G) for which the graph is hamiltonian.

scholarly journals Finding hidden hamiltonian cycles

1994 ◽  
Vol 5 (3) ◽  
pp. 395-410 ◽  
Author(s):  
Andrei Z. Broder ◽  
Alan M. Frieze ◽  
Eli Shamir
Keyword(s):  
Hamiltonian Cycles

4-connected polyhedra have at least a linear number of hamiltonian cycles

2021 ◽  
Vol 97 ◽  
pp. 103395
Author(s):  
Gunnar Brinkmann ◽  
Nico Van Cleemput
Keyword(s):  
Hamiltonian Cycles

Hamiltonian cycles and paths in faulty twisted hypercubes

2019 ◽  
Vol 257 ◽  
pp. 243-249
Author(s):  
Huiqing Liu ◽  
Xiaolan Hu ◽  
Shan Gao
Keyword(s):  
Hamiltonian Cycles
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