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An Ore-type sufficient condition for a bipancyclic ordering

1992
*
Discrete Mathematics
*

.,

doi:10.1016/0012-365x(92)90345-g
fatcat:bgwjjihw5ndvxewwrcexploii4
*An**Ore*-*type**sufficient**condition**for**a**bipancyclic**ordering*, Discrete Mathematics 102 (1992) 47-49. ...*A*weaker*sufficient**condition**for*hamiltonicity was given by Chvatal [l] . ... Suppose that G satisfies the hypothesis but does not have*a**bipancyclic**ordering*. By the main result of [4] , G contains*a*4-cycle. Thus G contains*a*subgraph with*a**bipancyclic**ordering*. ...##
###
Page 3542 of Mathematical Reviews Vol. , Issue 93g
[page]

1993
*
Mathematical Reviews
*

T. (4-ABER)

*An**Ore*-*type**sufficient**condition**for**a**bipancyclic**ordering*. Discrete Math. 102 (1992), no. 1, 47-49. ... The graph G is said to have*a**bipancyclic**ordering*if the vertices of X and Y can be labeled {x;, x2,---, Xn} and {y1,2,°--,¥n}, respectively, so that*for*any 2<k <n, the induced subgraph with vertex set ...##
###
Forthcoming papers

1991
*
Discrete Mathematics
*

*A*

*condition*

*for*

*a*hamiltonian bipartite graph to be

*bipancyclic*Let G be

*a*hamiltonian bipartite graph of

*order*2n and let: C = (x" y" x1, y" . . , x" yn, x1) be

*a*hamiltonian cycle of G. ... Choudum, On forcibly connected graphic sequences

*sufficient*

*conditions*connected are ... Choudum, On forcibly connected graphic sequences

*sufficient*

*conditions*connected are Forthcoming papers James

*A*. ...

##
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Bipancyclic subgraphs in random bipartite graphs
[article]

2012
*
arXiv
*
pre-print

*A*bipartite graph on 2n vertices is

*bipancyclic*if it contains cycles of all even lengths from 4 to 2n. ... Our result extends

*a*classical theorem of Mitchem and Schmeichel. ...

*A*variety of

*sufficient*

*conditions*

*for*

*a*Hamiltonian bipartite graph to be

*bipancyclic*have been studied in the literature, including [1, 2, 12, 13] and [15] . ...

##
###
On dominating pair degree conditions for hamiltonicity in balanced bipartite digraphs
[article]

2020
*
arXiv
*
pre-print

We prove several new

arXiv:2005.01466v1
fatcat:mezn24c2gje3tlh5unjjpwi6im
*sufficient**conditions**for*hamiltonicity and*bipancyclicity*in balanced bipartite digraphs, in terms of sums of degrees over dominating*or*dominated pairs of vertices. ... Consequently,*for*all but finitely many exceptional digraphs satifying*condition*(B k ) of this*type*, hamiltonicity implies*bipancyclicity*: It would be therefore very interesting to know whether*condition*... max{1, λ*a*} < k ≤*a*2 , and*for*every dominating pair {u, v} of vertices in D,d(u) ≥ 2a − k and d(v) ≥*a*+ k,*or*d(u) ≥*a*+ k and d(v) ≥ 2a − k ,then D is*bipancyclic**or*else*a*directed cycle of length ...##
###
Bipancyclic Subgraphs in Random Bipartite Graphs

2013
*
International Journal of Open Problems in Computer Science and Mathematics
*

*A*bipartite graph on 2n vertices is

*bipancyclic*if it contains cycles of all even lengths from 4 to 2n. ... Our result extends

*a*classical theorem of Mitchem and Schmeichel. ...

*A*variety of

*sufficient*

*conditions*

*for*

*a*Hamiltonian bipartite graph to be

*bipancyclic*have been studied in the literature, including [1, 2, 12, 13] and [15] . ...

##
###
Chorded pancyclicity in k-partite graphs
[article]

2018
*
arXiv
*
pre-print

.≥ n_k, the

arXiv:1801.07854v3
fatcat:hqxwzbyf5zc3fb6kediuqpopee
*condition*n_1≤p 2 is necessary and*sufficient**for*every subgraph of the complete k-partite graph K(n_1,... ... Our result implies that*for*any integers, k≥ 3 and n≥ 1,*a*balanced k-partite graph of*order*kn with has at least (k^2-k)n^2-2n(k-1)+4 2 edges is chorded pancyclic. ... We thank the MAA -Tensor Program*for*Women and Mathematics*for*facilitating*a*research visit during this project. ...##
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Ore and Erdős type conditions for long cycles in balanced bipartite graphs

2009
*
Discrete Mathematics & Theoretical Computer Science
*

Graphs and Algorithms International audience We conjecture

doi:10.46298/dmtcs.459
fatcat:c3vrsdf5ebdl3ihx43eq4tvwpy
*Ore*and Erdős*type*criteria*for**a*balanced bipartite graph of*order*2n to contain*a*long cycle C(2n-2k), where 0 <= k < n/2. ...*For*k = 0, these are the classical hamiltonicity criteria of Moon and Moser. The main two results of the paper assert that our conjectures hold*for*k = 1 as well. ... We would also like to thank Artur Fortuna*for**an*inspiring conversation. ...##
###
Edge condition for hamiltonicity in balanced tripartite graphs

2009
*
Opuscula Mathematica
*

We prove

doi:10.7494/opmath.2009.29.4.337
fatcat:moocevhmhbb3nlvefwmopfvej4
*an*analogous result*for*balanced tripartite graphs: If G is*a*balanced tripartite graph of*order*3n and size at least 3n 2 − 2n + 2, then G contains cycles of all lengths. ...*A*well-known theorem of Entringer and Schmeichel asserts that*a*balanced bipartite graph of*order*2n obtained from the complete balanced bipartite Kn,n by removing at most n − 2 edges, is*bipancyclic*. ... Acknowledgments I am happy to thank Lech Adamus*for*his valuable comments and discussions regarding the subject of this note. ...##
###
On the compatibility of the topologies of parallel tasks and computing systems
[article]

2020
*
arXiv
*
pre-print

of interconnect with

arXiv:2012.08079v1
fatcat:uqhmwqwg3rdlto5vjhszuqbvg4
*a*given topology*for*solving tasks with the same and different*types*of information topologies. ... The introduction of appropriate indexes based on the original topological model of parallel computations and on the nontraditional description of*a*graph by its projections is proposed and elucidated. ... However, the abstraction of such*a*model from the task's information topology and from the interconnect system topology hampers getting*a*complete picture*for*the*conditionality*of the task's parallelism ...##
###
Page 2463 of Mathematical Reviews Vol. , Issue 94e
[page]

1994
*
Mathematical Reviews
*

);
Luo, Sheng Zheng (PRC-HIT; Harbin)

*Sufficient**conditions**for*Hamiltonian graphs concerning neighborhood union and minimum degree. ... The authors show*for*n*sufficiently*large that R(K,,Z,) <n+k(k+1)(k+2)log,k. If in addition k is*an*odd prime power, then R(Ky, Z;,) <n+2k—2. ...##
###
Transversals and Bipancyclicity in Bipartite Graph Families

2021
*
Electronic Journal of Combinatorics
*

We also show that given

doi:10.37236/9489
fatcat:muktmrbxtfdnjox6qx6yk4wjla
*a*family $\mathcal G$ of $n$ bipartite graphs on*a*common set $X$ of $2n$ vertices meeting the same degree*conditions*, there exists*a*perfect matching on $X$ that uses exactly one ...*A*bipartite graph is called*bipancyclic*if it contains cycles of every even length from four up to the number of vertices in the graph. ... Acknowledgements I am grateful to Ladislav Stacho*for*making*a*suggestion to consider problems of pancyclicity in the setting of graph transversals and*for*carefully reading this paper. ...##
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Advances on the Hamiltonian Problem - A Survey

2003
*
Graphs and Combinatorics
*

This article is intended as

doi:10.1007/s00373-002-0492-x
fatcat:7isvoy4l6jfxxmeftkdcwoyhoy
*a*survey, updating earlier surveys in the area. ...*For*completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs ... Stacho [217] gave*a**sufficient**condition*of degree sum*type**for**a*graph to be hamiltonian. This*condition*generalizes several old results. ...##
###
Monochromatic paths and cycles in 2-edge-colored graphs with large minimum degree
[article]

2021
*
arXiv
*
pre-print

We prove that

arXiv:1906.02854v4
fatcat:iur6x7qalbcwjp525omjsko3om
*for*every*sufficiently*large n, if n = 3t+r where r ∈{0,1,2} and G is*an*n-vertex graph with δ(G) ≥ (3n-1)/4, then*for*every 2-edge-coloring of G, either there are cycles of every length ... Moreover, it implies*for**sufficiently*large n the conjecture by Benevides, Łuczak, Scott, Skokan and White that*for*n=3t+r where r ∈{0,1,2} and every n-vertex graph G with δ(G) ≥ 3n/4, in each 2-edge-coloring ... We thank the referees*for*their valuable comments. ...##
###
Cycles in graphs and related problems

2008
*
Dissertationes Mathematicae
*

In [249] the same authors studied the Dirac-

doi:10.4064/dm454-0-1
fatcat:nm4dk2d2xzdhvnhjt7t63uk6hu
*type**condition**for**bipancyclicity*. Theorem 4.63. Let G be*a*balanced bipartite graph of*order*2n. If δ(G) ≥ (n + 1)/2, then G is*bipancyclic*. ... [137] introduced*a*new*Ore*-*type**condition*. Theorem 3.45. ... From Theorem 6.28,*for*any m, 2 ≤ m ≤ 3p/4 + 6, there exists*a*(0, l)-path of length m. ...
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