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A characterization of pancyclic complements of line graphs

2005
*
Discrete Mathematics
*

We

doi:10.1016/j.disc.2004.02.024
fatcat:vat2lmpmzred5e3oijlzk5q5li
*characterize**graphs*G such that the*complements**of*their*line**graphs*are*pancyclic*. ... We*characterize*all*graphs*such that the*complement**graphs**of*their*line**graphs*are*pancyclic*or bi-*pancyclic*. ... For the class*of**complements**of**line**graphs*, our*characterization*provides the following linear time algorithm recognizing*pancyclic**complements**of**line**graphs*. Theorem 2.4. ...##
###
Forthcoming papers

1990
*
Discrete Mathematics
*

We give

doi:10.1016/0012-365x(90)90016-b
fatcat:ffwsvqnf3ncadcomjuau7e7lya
*a**characterization**of*directed branching greedoids. ... The following papers will be published in future issues: Wolfgang Schmidt, Greedoids and searches in directed*graphs*. Let (V, D) be*a*directed*graph*and PO E V. ... MacGillivray, On the product*of*the independent domination numbers*of**a**graph*and its*complement*. ...##
###
Contents

2005
*
Discrete Mathematics
*

Balbuena
Improved lower bound for the vertex connectivity

doi:10.1016/s0012-365x(05)00407-3
fatcat:rxvtxpybhzgy3krwwreznodnvy
*of*(d;g)-cages 162 J. Liu*A**characterization**of**pancyclic**complements**of**line**graphs*172 D. ... Horak On the chromatic number*of*Steiner triple systems*of*order 25 120 P. Horak and*A*. Rosa Extended Petersen*graphs*129 P.M. Kayll*A*note on weak Sidon sequences 141 S. ...##
###
Page 48 of Mathematical Reviews Vol. , Issue 80A
[page]

1980
*
Mathematical Reviews
*

For

*a**graph*G, let G and L(G) denote its*complement*and*line**graph*, respectively. It was shown in*a*previous paper by the author {Comment. Math. Univ. ... We give*a*sufficient condition for*a*connected*graph*G to contain at least two nonadjacent vertices*of*degree «(G), where x(G) denotes the connectivity*of*G.” 80a:05136 Nebesky, Ladislav On*pancyclic**line*...##
###
Forthcoming papers

1990
*
Discrete Mathematics
*

*A*well-known conjecture

*of*Thomassen says that every 4-connected

*line*

*graph*is hamiltonian. In this paper we prove that every 7-connected

*line*

*graph*is hamiltonian-connected. Michael 0. ... Berman, The number

*of*cut-vertices in

*a*

*graph*

*of*given minimum degree.

*A*

*graph*with n vertices and minimum degree k 2 2 can contain no more than (2k -2)n/(k2 -2) cut-vertices. ... Foumier and

*A*. Germa,

*Pancyclism*in hamiltonian

*graphs*. ...

##
###
Page 66 of Mathematical Reviews Vol. , Issue 97A
[page]

1997
*
Mathematical Reviews
*

After

*characterizing*the*graphs*G for which Gx K2 is Hamiltonian, we determine*a*criterion for extendability*of*cycles. ... Gendler (Clarion, PA) 97a:05136 05C40 Ando, Kiyoshi (J-CHOF-IF; Chofu); Kaneko, Atsusi |Kaneko, Atsushi] (J-KEIOE; Yokohama)*A*remark on the connectivity*of*the*complement**of**a*3-connected*graph*. ...##
###
Page 5293 of Mathematical Reviews Vol. , Issue 93j
[page]

1993
*
Mathematical Reviews
*

Moreover, we

*characterize*the*complements**of*weakly transitive orientable*graphs*as*a*special class*of*intersection*graphs**of*paths in planar*graphs*. ... Let H be*a**graph*that is not*a*path on four or fewer vertices, or the*complement**of*such*a*...##
###
Page 3971 of Mathematical Reviews Vol. , Issue 84j
[page]

1984
*
Mathematical Reviews
*

*A*

*characterization*

*of*these

*graphs*can be given by

*a*condition on the odd cycles: parity

*graphs*are just the

*graphs*in which every odd cycle has two crossing chords.

*A*theorem

*of*H. ... Authors’ summary: “

*A*

*graph*G is said to be biconnected if both G and its

*complement*G are connected.

*A*maximal biconnected induced subgraph

*of*G is called

*a*biconnected component

*of*G. ...

##
###
Page 5779 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

for any two non-adjacent edges e and e>, then the

*line**graph*L(G)*of*G is*pancyclic*. ... Trinajstié (Zagreb) 95j:05125 05C38 Liu, Chun Feng (PRC-JINZ; Jinzhou); Liang, Huai Xue*Pancyclicity**of**a*class*of**line**graphs*. (Chinese. English and Chinese summaries) Math. ...##
###
Cycles in graphs and related problems

2008
*
Dissertationes Mathematicae
*

Harary and Nash-Williams [164]

doi:10.4064/dm454-0-1
fatcat:nm4dk2d2xzdhvnhjt7t63uk6hu
*characterized*hamiltonian*line**graphs*in the following way. ... Another interesting problem relating to the notion*of*avd*graphs*is the*characterization**of*on-*line*arbitrarily vertex decomposable*graphs*. ... Case 1.1: |[*a*, g]| ≥ p − 2. By using the same method as in the proof*of*Lemma 6.32 we can show that F is*pancyclic*and contains*a*cycle*of*length p. ...##
###
Hamiltonicity and pancyclicity of cartesian products of graphs

2009
*
Discrete Mathematics
*

We extend known conditions for hamiltonicity and

doi:10.1016/j.disc.2008.11.024
fatcat:fuf5xpxx7bg3bkphfuatmmv5qq
*pancyclicity**of*the prism over*a**graph*G to the cartesian product*of*G with paths, cycles, cliques and general*graphs*. ... The cartesian product*of**a**graph*G with K 2 is called*a*prism over G. ... Acknowledgements We greatly appreciate the comments*of*all the anonymous referees. The first author's research was partially supported by grant no. 1M0021620808*of*the Czech Ministry*of*Education. ...##
###
Page 2404 of Mathematical Reviews Vol. , Issue 92e
[page]

1992
*
Mathematical Reviews
*

The main results

*of*this paper provide*a**characterization**of*change*graphs**of*edge-n-colorable bipartite multigraphs, n-regular bipartite multigraphs and trees. ... This theorem is also an extension*of**a*theorem*of*D. Amar, I. Fournier and*A*. Germa which states that*a**graph*G with x(G) >*a*(G) =2 is either*pancyclic*or isomorphic to C4 or C;. ...##
###
Lengths of Cycles in Generalized Pancake Graphs
[article]

2022
*
arXiv
*
pre-print

We prove that when the cyclic group has three elements the underlying, undirected

arXiv:2204.10494v1
fatcat:hc2pvjyc3rh27k4r6h32left5e
*graph**of*the generalized pancake*graph*is*pancyclic*, thus resembling*a*similar property*of*the pancake*graphs*and the burnt ... We furthermore show that the girth*of*the undirected generalized pancake*graphs*is min{m,8} if m≥3, thus*complementing*the known results for m=1,2. ...*A**graph*G = (V, E) is said to be*pancyclic*if it contains cycles*of*length k for every 3 ≤ k ≤ |V |. ...##
###
Page 6443 of Mathematical Reviews Vol. , Issue 95k
[page]

1995
*
Mathematical Reviews
*

*Line*

*graphs*are facet

*graphs*

*of*pure one-dimensional simplicial complexes. Cliques are complete subgraphs

*of*

*graphs*. ...

*A*

*graph*G = (V, E) is an interval

*graph*if its vertices can be put in

*a*one-to-one correspondence with

*a*family F

*of*intervals on the real

*line*such that two vertices are adjacent in G if and only if their ...

##
###
The property of edge-disjoint Hamiltonian cycles in transposition networks and hypercube-like networks

2015
*
Discrete Applied Mathematics
*

*A*

*graph*admits

*a*Hamiltonian decomposition if all

*of*its edges can be partitioned into disjoint Hamiltonian cycles. ... In this paper, we first study the property

*of*edge-disjoint Hamiltonian cycles in transposition networks which belong to

*a*subclass

*of*Cayley

*graphs*. ... Acknowledgments This work is partly supported by the National Science Council

*of*Taiwan under grant no. NSC 102-2221-E-324-007. ...

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