An Implicit Degree Condition for Cyclability in Graphs

2011 ◽  
pp. 82-89 ◽  
Author(s):  
Hao Li ◽  
Wantao Ning ◽  
Junqing Cai
Keyword(s):  
Degree Condition ◽  
Implicit Degree

An implicit degree condition for k-connected 2-heavy graphs to be hamiltonian

2018 ◽  
Vol 134 ◽  
pp. 9-13
Author(s):  
Junqing Cai ◽  
Hao Li ◽  
Yuzhong Zhang
Keyword(s):  
Degree Condition ◽  
Implicit Degree

An Implicit Degree Condition for Pancyclicity of Graphs

2012 ◽  
Vol 29 (5) ◽  
pp. 1459-1469 ◽  
Author(s):  
Hao Li ◽  
Junqing Cai ◽  
Wantao Ning
Keyword(s):  
Degree Condition ◽  
Implicit Degree

scholarly journals An implicit degree condition for hamiltonian graphs

2012 ◽  
Vol 312 (14) ◽  
pp. 2190-2196 ◽  
Author(s):  
Hao Li ◽  
Wantao Ning ◽  
Junqing Cai
Keyword(s):  
Hamiltonian Graphs ◽  
Degree Condition ◽  
Implicit Degree

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.

scholarly journals A sufficient degree condition for a graph to contain all trees of size k

2010 ◽  
Vol 27 (1) ◽  
pp. 135-140
Author(s):  
Camino Balbuena ◽  
Alberto Márquez ◽  
José Ramón Portillo
Keyword(s):  
Degree Condition ◽  
Sufficient Degree
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