A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A Short Proof of a Theorem Concerning Degree Sums and Connectivity on Hamiltonian Graphs

1999
*
Journal of combinatorial theory. Series B (Print)
*

proved that if G is

doi:10.1006/jctb.1998.1867
fatcat:6473xlvr5jfbhje7tvz34hw6dm
*a*2-*connected**graph*with n vertices such that d(u)+d(v)+d(w) n+} holds for any triple*of*independent vertices u, v,*and*w, then G is*hamiltonian*, where } is the vertex*connectivity*... In this note, we will give*a**short**proof**of*the above result. Academic Press ... The method we used in the*proof*may be applied in finding or proving other results which*concern**degree**sums**and*the*connectivity**of**graphs*. In order to prove*Theorem*2, we need the following. ...##
###
Depth first search in claw-free graphs

2017
*
Optimization Letters
*

The minimum

doi:10.1007/s11590-017-1211-0
fatcat:gy4etnasjfd2fnnz76jx7mkfqy
*degree**of*G is denoted by δ(G)*and*the minimum*sum**of**degrees**of*k independent vertices*of*G is denoted by δ k (G). ...*A**graph*G is traceable if it contains*a**hamiltonian*path. The minimum leaf number ml(G) is the minimum number*of*leaves (vertices*of**degree*1)*of*the spanning trees*of*G. ... Let G be*a**connected*claw-free*graph**of*diameter at most 2*and*let v be*a*non-cut vertex*of*G. Then there exists*a**hamiltonian*path*of*G starting at v.*Proof*. ...##
###
Dirac-type generalizations concerning large cycles in graphs

2009
*
Discrete Mathematics
*

Bondy conjectured

doi:10.1016/j.disc.2008.03.011
fatcat:vz3cqivbynerzgjdzcfadypykq
*a*common generalization*of*various results in*hamiltonian**graph*theory*concerning*Hamilton*and*dominating cycles by introducing*a*notion*of*PD λ -cycles (cycles that dominate all paths ... We present the reverse version*of*this result including*a**theorem**of*Voss*and*Zuluaga as*a*special case. ... Acknowledgments Many thanks to the anonymous referees for their helpful comments*and*suggestions, which have considerably improved the abstract*and*the introduction. ...##
###
On the minimum leaf number of cubic graphs
[article]

2018
*
arXiv
*
pre-print

We present new results

arXiv:1806.04451v1
fatcat:lmpfeivifjfcjfesl45dq4eunq
*concerning*the minimum leaf number*of*cubic*graphs*: we show that if $G$ is*a**connected*cubic*graph**of*order $n$, then $\mathrm{ml}(G) \leq \frac{n}6 + \frac13$, improving*on*the ... The \emph{minimum leaf number} $\hbox{ml} (G)$*of**a**connected**graph*$G$ is defined as the minimum number*of*leaves*of*the spanning trees*of*$G$. ... Acknowledgements Most*of*the computations were carried out using the Stevin Supercomputer Infrastructure at Ghent University. ...##
###
Page 2553 of Mathematical Reviews Vol. , Issue 84g
[page]

1984
*
Mathematical Reviews
*

Brooks’s

*theorem*states that*a*k-chromatic*graph*having no vertex*of**degree*>k must have*a*subgraph which is*a*complete k-*graph*. Two*short**proofs**of*Brooks’s*theorem*appear in the book by B. ... If g=1, so that G is*a*4-valent 3-*connected*simple*graph**on*the torus, then the minimum*of*the face-valency-*sums**of*its edges is at most 9,*and*can only be 9 if each edge is common to the boundaries*of*...##
###
Page 2093 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

The author gives

*a*sufficient condition,*of**degree*-*sum*type, for*a**graph*to be*Hamiltonian*. ...*One**of*the many consequences*of*this closure*theorem*is that*a*7-*connected*claw-free*graph*is*Hamiltonian*,*a*major step in proving the Matthews-Sumner con- jecture that*a*4-*connected*claw-free*graph*is ...##
###
More Progress on Tough Graphs - The Y2K Report

2002
*
Electronic Notes in Discrete Mathematics
*

We now know that not every 2-tough

doi:10.1016/s1571-0653(04)00055-1
fatcat:72x4yoepdjfwbcjt3rhgrksn7m
*graph*is*hamiltonian*. In fact for every > 0, there exists*a*(9/4− ) -tough nontraceable*graph*. ... We continue our quadrennial survey*of*results that relate the toughness*of**a**graph*to its cycle structure. ... The*degree**sum*condition can*of*course be converted to*a*weaker minimum*degree*condition.*Theorem*13 Let G be*a*1-tough*graph**on*n ≥ 11 vertices with δ ≥ n−4 2 . Then G is*hamiltonian*. Faudree et al ...##
###
Page 5191 of Mathematical Reviews Vol. , Issue 99h
[page]

1999
*
Mathematical Reviews
*

Francois Vanderseypen (Wijgmaal)
99h:05081 05C45 05C40
Wei, Bing [Wei, Bing'] (PRC-ASBJ-S; Beijing)

*A**short**proof**of**a**theorem**concerning**degree**sums**and**connectivity**on**Hamiltonian**graphs*. ... In this note, we give*a**short**proof**of*the above result.” ...##
###
Spanning Trees: A Survey

2010
*
Graphs and Combinatorics
*

We mainly deal with spanning trees having some particular properties

doi:10.1007/s00373-010-0973-2
fatcat:y6w7gmq5kfdula4heioxocsn3a
*concerning**a**hamiltonian*properties, for example, spanning trees with bounded*degree*, with bounded number*of*leaves, or with bounded ... In this paper, we give*a*survey*of*spanning trees. ... Acknowledgements The authors would like to thank the referees for their helpful comments*and*corrections. ...##
###
Toughness in Graphs – A Survey

2006
*
Graphs and Combinatorics
*

We begin our discussion with

doi:10.1007/s00373-006-0649-0
fatcat:pybxyua33rehpmiybdbj2cnzru
*a*well-known*theorem**of*Dirac [77].*Theorem*1. Let G be*a**graph**on*n ≥ 3 vertices with δ ≥ n 2 . Then G is*hamiltonian*. ... Toughness*and*Circumference In this section we survey results*concerning*the relationship between the toughness*of**a**graph**and*its circumference. ... After simplifying the*proof**of**Theorem*97 they used the result to obtain lower bounds*on*τ .*Theorem*98. Let G be*a**connected**graph*. ...##
###
Regular non-hamiltonian polyhedral graphs

2018
*
Applied Mathematics and Computation
*

Invoking Steinitz'

doi:10.1016/j.amc.2018.05.062
fatcat:hecq3pdksrb2xat7ssxjlh3v3a
*Theorem*, in the following*a*polyhedron shall be*a*3-*connected*planar*graph*. ... Let G be*a*polyhedron*of**connectivity*3*and*X The cubic case Tait conjectured [35] in 1884 that every cubic polyhedron is*hamiltonian*. ... Zamfirescu is supported by*a*Postdoctoral Fellowship*of*the Research Foundation Flanders (FWO). ...##
###
Page 1822 of Mathematical Reviews Vol. 53, Issue 6
[page]

1977
*
Mathematical Reviews
*

*Theorem*2: For every n

*and*k with n,k21, there exists an n-

*connected*

*graph*G such that XG* is non-

*Hamiltonian*. ... The author proves that the above condition is sufficient for k=5

*and*provides

*a*new,

*short*

*proof*

*of*the previously established

*theorem*that the conditions are sufficient for k=3 except for the case n=6 ...

##
###
On some intriguing problems in hamiltonian graph theory—a survey

2002
*
Discrete Mathematics
*

We survey results

doi:10.1016/s0012-365x(01)00325-9
fatcat:wcggfjuntbgrjmegqldzdz55hy
*and*open problems in*hamiltonian**graph*theory centered around three themes: regular*graphs*, t-tough*graphs*,*and*claw-free*graphs*. ... The*proof**of**Theorem*2.6 (via*Theorems*2.8*and*2.9) uses several ideas from [17] , where*a*relatively*short**proof**of*(an extension*of*)*Theorem*2.1 occurs. ...*degree**sums*. ...##
###
Supereulerian graphs: A survey

1992
*
Journal of Graph Theory
*

There is

doi:10.1002/jgt.3190160209
fatcat:tgp5puuagzf6pgdn7ng623zdzq
*a*reduction method to determine whether*a**graph*is supereulerian,*and*it can also be applied to study other concepts, e.g.,*hamiltonian*line*graphs*,*a*certain type*of*double cycle cover,*and*the ... total interval number*of**a**graph*. ... By Corollary 5.1A, Corollary 3.2A,*and*(*a*)*of**Theorem*2.2, the line*graph**of*any 4-edge-*connected**graph*is*hamiltonian*. ...##
###
Page 2345 of Mathematical Reviews Vol. , Issue 2002D
[page]

2002
*
Mathematical Reviews
*

The main result gives

*a*minimum*degree*condition*and**a**sum**of**degrees*condition*on**a*bipartite*graph*either*of*which implies the existence*of**a*2-factor with each cycle*of*the 2-factor containing*a*specified ... each*of*its longest cycles (without all being*Hamiltonian*).” 2002d:05077 05C38 05C35 Schrijver, Alexander (NL-MATH; Amsterdam)*A**short**proof**of*Mader’s .7-paths*theorem*. ...
« Previous

*Showing results 1 — 15 out of 6,340 results*