A new neighborhood union condition for Hamiltonian graphs

1997 ◽  
Vol 13 (2) ◽  
pp. 187-192
Author(s):  
Wei Bing ◽  
Zhu Yongjin
Keyword(s):  
Hamiltonian Graphs ◽  
Union Condition ◽  
Neighborhood Union Condition ◽  
Neighborhood Union

scholarly journals Color Neighborhood Union Conditions for Long Heterochromatic Paths in Edge-Colored Graphs

10.37236/995 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
He Chen ◽  
Xueliang Li
Keyword(s):  
Lower Bound ◽  
Colored Graph ◽  
Colored Graphs ◽  
Union Condition ◽  
Neighborhood Union Condition ◽  
Color Neighborhood ◽  
Neighborhood Union

Let $G$ be an edge-colored graph. A heterochromatic (rainbow, or multicolored) path of $G$ is such a path in which no two edges have the same color. Let $CN(v)$ denote the color neighborhood of a vertex $v$ of $G$. In a previous paper, we showed that if $|CN(u)\cup CN(v)|\geq s$ (color neighborhood union condition) for every pair of vertices $u$ and $v$ of $G$, then $G$ has a heterochromatic path of length at least $\lfloor{2s+4\over5}\rfloor$. In the present paper, we prove that $G$ has a heterochromatic path of length at least $\lceil{s+1\over2}\rceil$, and give examples to show that the lower bound is best possible in some sense.

scholarly journals A note on the transmission feasibility problem in networks

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 889-895
Author(s):  
Wei Gao ◽  
Yunqing Zhang ◽  
Yaojun Chen
Keyword(s):  
Data Transmission ◽  
Independent Set ◽  
Feasibility Problem ◽  
Network Graph ◽  
Graph Problems ◽  
Union Condition ◽  
Neighborhood Union Condition ◽  
Entire Network ◽  
Neighborhood Union ◽  
The Ideal

Abstract In the networking designing phase, the network needs to be built according to certain indicators to ensure that the network has the ideal functions and can work smoothly. From a modeling perspective, each site in the network is represented by a vertex, channels between sites are represented by edges, and thus the entire network can be denoted as a graph. Problems in the network can be transformed into corresponding graph problems. In particular, the feasibility of data transmission can be transformed into the existence of fractional factors in network graph. This note gives an independent set neighborhood union condition for the existence of fractional factors in a special setting, and shows that the neighborhood union condition is sharp.

Hamiltonian graphs involving distances

1992 ◽  
Vol 16 (2) ◽  
pp. 121-129 ◽  
Author(s):  
Guantao Chen ◽  
R. H. Schelp
Keyword(s):  
Hamiltonian Graphs

Two theorems on Hamiltonian graphs

1984 ◽  
Vol 35 (1) ◽  
pp. 32-35 ◽  
Author(s):  
A. S. Asratyan ◽  
N. K. Khachatryan
Keyword(s):  
Hamiltonian Graphs
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