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A condition for a hamiltonian bipartite graph to be bipancyclic

1992
*
Discrete Mathematics
*

But if the

doi:10.1016/0012-365x(92)90116-w
fatcat:2ukehq4yyzex5iiiflo7ow4pli
*graph*is supposed*to**be**hamiltonian*, we need weaker*conditions*in order*for*the*graph**to**be*pancyclic [l, 31 . When G is*a*balanced*bipartite**graph*, we have analogous results [9-111. ... Introduction Let G*be**a*finite*graph*of order n. Various sufficient*conditions**for**a**graph**to**be**hamiltonian*have been given in terms of vertex-degree and size of the*graph*[5-81. ...##
###
Applying a condition for a hamiltonian bipartite graph to be bipancyclic

1993
*
Discrete Mathematics
*

., Applying

doi:10.1016/0012-365x(93)90136-h
fatcat:olgtucxxjzeabeuhdclxpfjufm
*a**condition**for**a**hamiltonian**bipartite**graph**to**be**bipancyclic*, Discrete Mathematics 111 (1993) 19-25. ... sufficient*for*the*graph**to**be**bipancyclic*. ... Sufficient*conditions**for**a**bipartite**graph**to**be**bipancyclic*In*bipartite**graphs*, the following theorem gives*a**condition*Theorem 1.1*for**a**hamiltonian**bipartite**graph**to**be**bipancyclic*. similar*to*that ...##
###
Spectral Conditions for the Bipancyclic Bipartite Graphs
[article]

2021
*
arXiv
*
pre-print

G is said

arXiv:2106.13741v1
fatcat:yzwp66subjgellbtc5yfdp6yrm
*to**be**bipancyclic*if it contains cycles of every even length from 4*to*|V(G)|. In this note, we present spectral*conditions**for*the*bipancyclic**bipartite**graphs*. ... Let G = (X, Y; E)*be**a**bipartite**graph*with two vertex partition subsets X and Y. G is said*to**be*balanced if |X| = |Y|. ... The*bipartite**graph*G is said*to**be*balanced if |V 1 | = |V 2 |. Clearly, if*a**bipartite**graph*is*Hamiltonian*, then it must*be*balanced. ...##
###
Spectral conditions for the Bipancyclic Bipartite graphs

2021
*
Open Journal of Discrete Applied Mathematics
*

In this note, we present spectral

doi:10.30538/psrp-odam2021.0058
fatcat:46qi5a747vettjh74guuvrxs7i
*conditions**for*the*bipancyclic**bipartite**graphs*. ... Let \(G = (X, Y; E)\)*be**a**bipartite**graph*with two vertex partition subsets \(X\) and \(Y\). ... The*bipartite**graph*G is said*to**be*balanced if V 1 = V 2 . Clearly, if*a**bipartite**graph*is*Hamiltonian*, then it must*be*balanced. ...##
###
An Ore-type sufficient condition for a bipancyclic ordering

1992
*
Discrete Mathematics
*

., An Ore-type sufficient

doi:10.1016/0012-365x(92)90345-g
fatcat:bgwjjihw5ndvxewwrcexploii4
*condition**for**a**bipancyclic*ordering, Discrete Mathematics 102 (1992) 47-49. ...*A*weaker sufficient*condition**for*hamiltonicity was given by Chvatal [l] . ... Let G(X, Y, E)*be**a*balanced*bipartite**graph*of order 2n 2 4 satisfying*a*(G)>n+l. (1) 0012-365X/92/$05.00 0 1992-Elsevier Science Publishers B.V. ...##
###
On the cycle structure of hamiltonian k-regular bipartite graphs of order 4k
[article]

2009
*
arXiv
*
pre-print

Moreover, if such

arXiv:0711.4426v3
fatcat:peu7fsi2rbd6jf7bi45hd3dbju
*a*cycle can*be*chosen*to*omit*a*pair of adjacent vertices, then G is*bipancyclic*. ... It is shown that*a**hamiltonian*n/2-regular*bipartite**graph*G of order 2n>8 contains*a*cycle of length 2n-2. ... In [2] , Entringer and Schmeichel gave*a*sufficient*condition**for**a**hamiltonian**bipartite**graph**to**be**bipancyclic*. Theorem 1. ...##
###
Highly fault-tolerant cycle embeddings of hypercubes

2007
*
Journal of systems architecture
*

In this paper, we first prove that the n-dimensional hypercube is 2n

doi:10.1016/j.sysarc.2006.10.008
fatcat:wzjf4of2wvcq7gm6kgy3ewzjyq
*À*5*conditional*fault-*bipancyclic*. ... That is, an injured hypercube with up*to*2n*À*5 faulty links has*a*cycle of length l*for*every even 4 6 l 6 2 n when each node of the hypercube is incident with at least two healthy links. ...*A**bipartite**graph*G is k*conditional*edge fault-tolerant*bipancyclic*(abbreviated as k*conditional*fault-*bipancyclic*) if G*À*F is*bipancyclic**for*every F with jFj 6 k under the*condition*that every vertex ...##
###
Transversals and bipancyclicity in bipartite graph families
[article]

2021
*
arXiv
*
pre-print

*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*. ... We also show that given

*a*family 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 edge from each ... Therefore, Theorem 1.2 may

*be*summarized by stating that

*a*balanced

*bipartite*

*graph*meeting certain minimum degree

*conditions*is

*bipancyclic*. ...

##
###
A Meyniel-Type Condition for Bipancyclicity in Balanced Bipartite Digraphs

2018
*
Graphs and Combinatorics
*

We prove that

doi:10.1007/s00373-018-1907-7
fatcat:i4t6gvlkvjhrfdox247xyx43sm
*a*strongly connected balanced*bipartite*digraph D of order 2a,*a*≥3, satisfying d(u)+d(v)≥ 3a*for*every pair of vertices u,v with*a*common in-neighbour or*a*common out-neighbour, is either ...*bipancyclic*or*a*directed cycle of length 2a. ... Acknowledgments The author is grateful*to*an anonymous referee*for*spotting*a*critical mistake in an earlier version of the manuscript. ...##
###
Survey on path and cycle embedding in some networks

2009
*
Frontiers of Mathematics in China
*

Obviously, an edgepancyclic

doi:10.1007/s11464-009-0017-5
fatcat:sizti6s4pvfazgyrijnfvomwra
*graph*is certainly vertex-pancyclic.*A**graph*G is said*to**be**hamiltonian*connected if there exists*a**hamiltonian*path between any two vertices of G [122] . ...*A**graph*G of order n is said*to**be*panconnected if*for*any pair of different vertices x and y with distance d in G, there exist xy-paths of every length from d*to*n − 1 [5, 151] .*A**graph*... Acknowledgements As an invited speaker, the first author partially reported this work at the International Workshop on Structures and Cycles in*Graphs*, 5-9 July 2005, Wuhan, ...##
###
New sufficient conditions for bipancyclic bipartite graphs

2004
*
Discrete Mathematics
*

We give here two su cient

doi:10.1016/j.disc.2003.11.039
fatcat:6yw2giakgbgz7oqiwry4sypcrq
*conditions**for**a**bipartite*balanced*graph*of order 2n*to**be**bipancyclic*. ... one is*for**bipartite*balanced traceable*graphs*containing an*hamiltonian*path whose extremities are nonadjacent and have degree sum at least n + 1. ... We then give two new su cient*conditions**for**a**bipartite*balanced*graph**to**be**bipancyclic*. ...##
###
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. ... In this paper we prove that the random

*bipartite*

*graph*G(n,n,p) with p(n)≫ n^-2/3 asymptotically almost surely has the following resilience property: Every

*Hamiltonian*subgraph G' of G(n,n,p) with more ...

*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] . ...

##
###
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. ... In this paper we prove that the random

*bipartite*

*graph*G(n, n, p) with p(n) n −2/3 asymptotically almost surely has the following resilience property: Every

*Hamiltonian*subgraph G of G(n, n, p) with more ...

*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] . ...

##
###
Page 5360 of Mathematical Reviews Vol. , Issue 92j
[page]

1992
*
Mathematical Reviews
*

*A*

*bipartite*

*graph*of even order is

*bipancyclic*if it contains cycles of all possible even lengths. The authors consider here

*a*conjecture due

*to*J. Mitchem and E. F. ... The authors generalize this result by proving it

*to*

*be*true when mp < n < d(u)+ d(v)+

*a*, where

*a*> 4, and they obtain bounds

*for*c(G) and n— c(G)

*for*such

*graphs*. ...

##
###
Linear array and ring embeddings in conditional faulty hypercubes

2004
*
Theoretical Computer Science
*

Based on this requirement, we prove that Qn contains

doi:10.1016/j.tcs.2004.01.035
fatcat:tiqt3hyfmngcdgt6vppjtrw4fi
*a**hamiltonian*path joining any two di erent colored vertices even if it has up*to*2n − 5 edge faults. ... The n-dimensional hypercube Qn is*a**graph*having 2 n vertices labeled from 0*to*2 n − 1. Two vertices are connected by an edge if their binary labels di er in exactly one bit position. ...*A**bipartite**graph*G = (V 0 ; V 1 ; E) is said*to**be*equitable if and only if |V 0 | = |V 1 |, and Simmons [10] introduced the concept of*hamiltonian*laceability*for*those equitable*bipartite**graphs*. ...
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