scholarly journals Neighborhood-union condition for an [a,b]-factor avoiding a specified Hamiltonian cycle

2017 ◽  
Vol 340 (6) ◽  
pp. 1419-1425 ◽  
Author(s):  
Michitaka Furuya ◽  
Takamasa Yashima
Keyword(s):  
Hamiltonian Cycle ◽  
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.

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.

A Parallel Reduction of Hamiltonian Cycle to Hamiltonian Path in Tournaments

1995 ◽  
Vol 19 (3) ◽  
pp. 432-440 ◽  
Author(s):  
E. Bampis ◽  
M. Elhaddad ◽  
Y. Manoussakis ◽  
M. Santha
Keyword(s):  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Parallel Reduction
Sign in / Sign up

Export Citation Format

Share Document