Hamiltonian cycle curves in the space of discounted occupational measures

2015 ◽  
Author(s):  
Jerzy A. Filar ◽  
Asghar Moeini
Keyword(s):  
Hamiltonian Cycle ◽  
Occupational Measures

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

A New Link-Based Hamiltonian Cycle Protection in Survivable WDM Optical Networks

2008 ◽  
Author(s):  
Lei Guo ◽  
Xingwei Wang ◽  
Xuetao Wei ◽  
Ting Yang ◽  
Weigang Hou ◽  
...  
Keyword(s):  
Optical Networks ◽  
Hamiltonian Cycle ◽  
Wdm Optical Networks

scholarly journals Approximating Cayley Diagrams Versus Cayley Graphs

2012 ◽  
Vol 21 (4) ◽  
pp. 635-641
Author(s):  
ÁDÁM TIMÁR
Keyword(s):  
Cayley Graph ◽  
Hamiltonian Cycle ◽  
Cayley Graphs ◽  
The Other ◽  
Finite Graphs ◽  
Similar Construction ◽  
Graph Property

We construct a sequence of finite graphs that weakly converge to a Cayley graph, but there is no labelling of the edges that would converge to the corresponding Cayley diagram. A similar construction is used to give graph sequences that converge to the same limit, and such that a Hamiltonian cycle in one of them has a limit that is not approximable by any subgraph of the other. We give an example where this holds, but convergence is meant in a stronger sense. This is related to whether having a Hamiltonian cycle is a testable graph property.

scholarly journals Study to evaluate the effectiveness of stress management workshops on response to general and occupational measures of stress

1999 ◽  
Vol 49 (7) ◽  
pp. 451-457 ◽  
Author(s):  
R. J. L. Heron ◽  
S. McKeown ◽  
J. A. Tomenson ◽  
E. L. Teasdale
Keyword(s):  
Stress Management ◽  
Occupational Measures

Hamiltonian cycle and path embeddings in 3-ary n-cubes based on K1,3-structure faults

2018 ◽  
Vol 120 ◽  
pp. 148-158 ◽  
Author(s):  
Yali Lv ◽  
Cheng-Kuan Lin ◽  
Jianxi Fan ◽  
Xiaohua Jia
Keyword(s):  
Hamiltonian Cycle

scholarly journals Semi-Degree Threshold for Anti-Directed Hamiltonian Cycles

10.37236/3610 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Louis DeBiasio ◽  
Theodore Molla
Keyword(s):  
Directed Graph ◽  
Hamiltonian Cycle ◽  
Minimum Degree ◽  
Directed Graphs ◽  
Hamiltonian Cycles ◽  
Alternate Direction ◽  
Degree Conditions

In 1960 Ghouila-Houri extended Dirac's theorem to directed graphs by proving that if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $n/2$, then $D$ contains a directed Hamiltonian cycle. For directed graphs one may ask for other orientations of a Hamiltonian cycle and in 1980 Grant initiated the problem of determining minimum degree conditions for a directed graph $D$ to contain an anti-directed Hamiltonian cycle (an orientation in which consecutive edges alternate direction). We prove that for sufficiently large even $n$, if $D$ is a directed graph on $n$ vertices with minimum out-degree and in-degree at least $\frac{n}{2}+1$, then $D$ contains an anti-directed Hamiltonian cycle. In fact, we prove the stronger result that $\frac{n}{2}$ is sufficient unless $D$ is one of two counterexamples. This result is sharp.

scholarly journals Vizing's 2-Factor Conjecture Involving Toughness and Maximum Degree Conditions

10.37236/7353 ◽  
2019 ◽  
Vol 26 (2) ◽  
Author(s):  
Jinko Kanno ◽  
Songling Shan
Keyword(s):  
Maximum Degree ◽  
Hamiltonian Cycle ◽  
Simple Graph ◽  
Chromatic Index ◽  
New Techniques ◽  
Critical Graph ◽  
Degree Conditions ◽  
Delta G ◽  
Proper Subgraph

Let $G$ be a simple graph, and let $\Delta(G)$ and $\chi'(G)$ denote the maximum degree and chromatic index of $G$, respectively. Vizing proved that $\chi'(G)=\Delta(G)$ or $\chi'(G)=\Delta(G)+1$. We say $G$ is $\Delta$-critical if $\chi'(G)=\Delta(G)+1$ and $\chi'(H)<\chi'(G)$ for every proper subgraph $H$ of $G$. In 1968, Vizing conjectured that if $G$ is a $\Delta$-critical graph, then  $G$ has a 2-factor. Let $G$ be an $n$-vertex $\Delta$-critical graph. It was proved that if $\Delta(G)\ge n/2$, then $G$ has a 2-factor; and that if $\Delta(G)\ge 2n/3+13$, then $G$  has a hamiltonian cycle, and thus a 2-factor. It is well known that every 2-tough graph with at least three vertices has a 2-factor. We investigate the existence of a 2-factor in a $\Delta$-critical graph under "moderate" given toughness and  maximum degree conditions. In particular, we show that  if $G$ is an  $n$-vertex $\Delta$-critical graph with toughness at least 3/2 and with maximum degree at least $n/3$, then $G$ has a 2-factor. We also construct a family of graphs that have order $n$, maximum degree $n-1$, toughness at least $3/2$, but have no 2-factor. This implies that the $\Delta$-criticality in the result is needed. In addition, we develop new techniques in proving the existence of 2-factors in graphs.

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