scholarly journals A common generalization of Chvátal-Erdős' and Fraisse's sufficient conditions for hamiltonian graphs

1995 ◽  
Vol 142 (1-3) ◽  
pp. 1-19 ◽  
Author(s):  
A. Ainouche
Keyword(s):  
Sufficient Conditions ◽  
Hamiltonian Graphs ◽  
Common Generalization

scholarly journals Commutators in groups of order-preserving permutations

1991 ◽  
Vol 33 (1) ◽  
pp. 55-59 ◽  
Author(s):  
Manfred Droste ◽  
R. M. Shortt
Keyword(s):  
Automorphism Group ◽  
Normal Subgroup ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Homogeneous Tree ◽  
Common Generalization ◽  
Partially Ordered ◽  
Bounded Support ◽  
Locally Linear

Let (S, ≤) be a poset (partially ordered set), A(S) = Aut(S, ≤) its automorphism group and G ⊆ A(S) a subgroup. In the literature, various authors have studied sufficient conditions on G and the structure of (S, ≤) which imply that G is simple or perfect. Let us call (S, ≤) doubly homogeneous if each isomorphism between two 2-subsets of 5 extends to an isomorphism of (S, ≤). Higman [8] proved that if (S, ≤) is a doubly homogeneous chain then B(S), the group of all automorphisms of (S, ≤) with bounded support, is simple, and each element of B(S) is a commutator in B(S). Droste, Holland and Macpherson [5] showed that if (S, ≤) is a doubly homogeneous tree then its automorphism group again contains a unique simple normal subgroup in which each element is a commutator. Dlab [3] established similar results for various groups of locally linear automorphisms of the reals. Further results in this direction are contained in Glass [7]. It is the aim of this note to establish a common generalization and sharpening of the previously mentioned results.

WIENER INDEX ON TRACEABLE AND HAMILTONIAN GRAPHS

2016 ◽  
Vol 94 (3) ◽  
pp. 362-372 ◽  
Author(s):  
RUIFANG LIU ◽  
XUE DU ◽  
HUICAI JIA
Keyword(s):  
Bipartite Graph ◽  
Spectral Radius ◽  
Sufficient Conditions ◽  
Wiener Index ◽  
Hamiltonian Graphs

We give sufficient conditions for a graph to be traceable and Hamiltonian in terms of the Wiener index and the complement of the graph, which correct and extend the result of Yang [‘Wiener index and traceable graphs’, Bull. Aust. Math. Soc.88 (2013), 380–383]. We also present sufficient conditions for a bipartite graph to be traceable and Hamiltonian in terms of its Wiener index and quasicomplement. Finally, we give sufficient conditions for a graph or a bipartite graph to be traceable and Hamiltonian in terms of its distance spectral radius.

Hamiltonian Paths and Cycles

2013 ◽  
pp. 96-105
Author(s):  
Mahtab Hosseininia ◽  
Faraz Dadgostari
Keyword(s):  
Hamiltonian Cycle ◽  
Travelling Salesman Problem ◽  
Sufficient Conditions ◽  
Hamiltonian Cycles ◽  
Hamiltonian Graph ◽  
Hamiltonian Graphs ◽  
Hamiltonian Paths ◽  
Graph Problems ◽  
History Of ◽  
Knight’S Tour

In this chapter, the concepts of Hamiltonian paths and Hamiltonian cycles are discussed. In the first section, the history of Hamiltonian graphs is described, and then some concepts such as Hamiltonian paths, Hamiltonian cycles, traceable graphs, and Hamiltonian graphs are defined. Also some most known Hamiltonian graph problems such as travelling salesman problem (TSP), Kirkman’s cell of a bee, Icosian game, and knight’s tour problem are presented. In addition, necessary and (or) sufficient conditions for existence of a Hamiltonian cycle are investigated. Furthermore, in order to solve Hamiltonian cycle problems, some algorithms are introduced in the last section.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Sign in / Sign up

Export Citation Format

Share Document