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A characterization of pancyclic complements of line graphs

Jiping Liu
2005 Discrete Mathematics  
We 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.  ... 
doi:10.1016/j.disc.2004.02.024 fatcat:vat2lmpmzred5e3oijlzk5q5li

Forthcoming papers

1990 Discrete Mathematics  
We give 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.  ... 
doi:10.1016/0012-365x(90)90016-b fatcat:ffwsvqnf3ncadcomjuau7e7lya

Contents

2005 Discrete Mathematics  
Balbuena Improved lower bound for the vertex connectivity 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.  ... 
doi:10.1016/s0012-365x(05)00407-3 fatcat:rxvtxpybhzgy3krwwreznodnvy

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.  ... 
doi:10.1016/0012-365x(90)90069-t fatcat:wzbr5q4ikzhxxb4lvuteckukqm

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

Antoni Marczyk
2008 Dissertationes Mathematicae  
Harary and Nash-Williams [164] 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.  ... 
doi:10.4064/dm454-0-1 fatcat:nm4dk2d2xzdhvnhjt7t63uk6hu

Hamiltonicity and pancyclicity of cartesian products of graphs

Roman Čada, Evelyne Flandrin, Hao Li
2009 Discrete Mathematics  
We extend known conditions for hamiltonicity and 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.  ... 
doi:10.1016/j.disc.2008.11.024 fatcat:fuf5xpxx7bg3bkphfuatmmv5qq

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]

Saúl A. Blanco, Charles Buehrle
2022 arXiv   pre-print
We prove that when the cyclic group has three elements the underlying, undirected 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 |.  ... 
arXiv:2204.10494v1 fatcat:hc2pvjyc3rh27k4r6h32left5e

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

Ruo-Wei Hung
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.  ... 
doi:10.1016/j.dam.2014.09.006 fatcat:fz2efvsmqjfgpjhrwukkpqt6sa
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