A Note on Dominating Pair Degree Condition for Hamiltonian Cycles in Balanced Bipartite Digraphs

2021 ◽  
Vol 38 (1) ◽  
Author(s):  
Ruixia Wang
Keyword(s):  
Hamiltonian Cycles ◽  
Degree Condition

scholarly journals Minimum pair degree condition for tight Hamiltonian cycles in 4-uniform hypergraphs

2020 ◽  
Vol 161 (2) ◽  
pp. 647-699
Author(s):  
J. Polcyn ◽  
Chr. Reiher ◽  
V. Rödl ◽  
A. Ruciński ◽  
M. Schacht ◽  
...  
Keyword(s):  
Hamiltonian Cycles ◽  
Degree Condition ◽  
Uniform Hypergraphs

scholarly journals Minimum vertex degree condition for tight Hamiltonian cycles in 3‐uniform hypergraphs

2019 ◽  
Vol 119 (2) ◽  
pp. 409-439 ◽  
Author(s):  
Christian Reiher ◽  
Vojtěch Rödl ◽  
Andrzej Ruciński ◽  
Mathias Schacht ◽  
Endre Szemerédi
Keyword(s):  
Vertex Degree ◽  
Hamiltonian Cycles ◽  
Degree Condition ◽  
Uniform Hypergraphs

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 Degree and neighborhood intersection conditions restricted to induced subgraphs ensuring Hamiltonicity of graphs

2014 ◽  
Vol 06 (03) ◽  
pp. 1450043
Author(s):  
Bo Ning ◽  
Shenggui Zhang ◽  
Bing Chen
Keyword(s):  
Hamilton Cycles ◽  
Induced Subgraphs ◽  
Degree Sum ◽  
Degree Condition

Let claw be the graph K1,3. A graph G on n ≥ 3 vertices is called o-heavy if each induced claw of G has a pair of end-vertices with degree sum at least n, and called 1-heavy if at least one end-vertex of each induced claw of G has degree at least n/2. In this note, we show that every 2-connected o-heavy or 3-connected 1-heavy graph is Hamiltonian if we restrict Fan-type degree condition or neighborhood intersection condition to certain pairs of vertices in some small induced subgraphs of the graph. Our results improve or extend previous results of Broersma et al., Chen et al., Fan, Goodman and Hedetniemi, Gould and Jacobson, and Shi on the existence of Hamilton cycles in graphs.

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