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Page 2310 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
The switching class [G] determined by G consists of all vertex switchings G4 for subsets A C V. We prove that the trees of a switching class [G] are isomorphic to each other.  ...  We also determine the types of trees T that have isomorphic copies in [G]. Finally we show that apart from one exceptional type of forest, the real forests in a switching class are isomorphic.  ... 

Vertex pancyclic graphs

Bert Randerath, Ingo Schiermeyer, Meike Tewes, Lutz Volkmann
2002 Discrete Applied Mathematics  
In this paper, we shall present di erent su cient conditions for graphs to be vertex pancyclic. ?  ...  A graph G is called pancyclic if it contains a cycle of length k for every 3 6 k 6 n, and it is called vertex pancyclic if every vertex is contained in a cycle of length k for every 3 6 k 6 n.  ...  We deÿne a very important family H ; n of graph classes which will be useful in the following to provide bounds for vertex pancyclicity and fully extendability. Remark 8.  ... 
doi:10.1016/s0166-218x(01)00292-x fatcat:fesqsyyg6ff7no23v34htxbi7y

Pancyclic properties of the graph of some 0–1 polyhedra

Denis Naddef
1984 Journal of combinatorial theory. Series B (Print)  
In this paper it is shown that a certain class of (&l) polyhedra, which includes the matroid basis polytopes and the perfect matching polytopes, have graphs with the property that the edges, under a certain  ...  This class will be defined in the next section, where the basic concepts on polyhedra with O-l valued vertices are recalled.  ...  pancyclic and not pancyclic (except if p = 3, in which case they are pancyclic).  ... 
doi:10.1016/0095-8956(84)90040-6 fatcat:p5zqiqu7efei7i4y6fiwjf2v44

The Directed Anti-Oberwolfach Solution: Pancyclic 2-Factorizations of Complete Directed Graphs of Odd Order

Brett Stevens
2002 Electronic Journal of Combinatorics  
The directed anti-Oberwolfach problem asks for a 2-factorization (each factor has in-degree 1 and out-degree 1 for a total degree of two) of $K_{2n+1}$, not with consistent cycle components in each 2-factor  ...  like the Oberwolfach problem, but such that every admissible cycle size appears at least once in some 2-factor.  ...  In this definition, when n < 4, or n − 2 < 2, then the only admissible cycle size is n and the pancyclic 2-factorizations in these cases are trivial.  ... 
doi:10.37236/1633 fatcat:sl7smrkf5fftzhoj2ahtgkuqua

Page 1491 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
in switching classes.  ...  We show that every switching class, except the class of all complete bipartite graphs, contains a pancyclic graph.  ... 

Page 3258 of Mathematical Reviews Vol. 58, Issue 5 [page]

1979 Mathematical Reviews  
The vanishing of these in- variants has combinatorial significance. For example, y =0 if and only if there is a graph in the switching class which admits G as an automorphism group.  ...  Equivalent concepts are switching classes of graphs, double coverings of complete graphs, and depen- dent sets of equiangular lines in Euclidean space.  ... 

Contents

2004 Discrete Mathematics  
Volkmann Vertex 6-pancyclic in-tournaments 227 -365X/04/$ -see front matter doi:10.1016/S0012-365X(04)00280-8  ...  Das Maximizing the sum of the squares of the degrees of a graph 57 On integral graphs which belong to the class aK a ,bK b;b 183 N.  ... 
doi:10.1016/s0012-365x(04)00280-8 fatcat:gv6egom3pffcjhh2yfx5bvnycq

The anti-Oberwolfach solution: pancyclic 2-factorizations of complete graphs

Brett Stevens
2003 Theoretical Computer Science  
We pose and completely solve the existence of pancyclic 2-factorizations of complete graphs and complete bipartite graphs.  ...  The pancyclic problem is intended to showcase the power this method o ers to solve a wide range of 2-factorization problems.  ...  Indeed, the pancyclic question is recreational in nature but we use it as a convenient context in which to present powerful and very serious construction methods that can contribute to a broader class  ... 
doi:10.1016/s0304-3975(02)00650-3 fatcat:ibknop4eujdthk4o3js235baye

The dimension of the negative cycle vectors of a signed graph

Alex Schaefer, Thomas Zaslavsky
2019 Ars Mathematica Contemporanea  
Let SpecC(Γ) denote the list of lengths of cycles in Γ. We equip each signed graph with a vector whose entries are the numbers of negative k-cycles for k ∈ SpecC(Γ).  ...  Using matchings with a strong permutability property, we provide lower bounds on the dimension of this space; in particular, we show for complete graphs, complete bipartite graphs, and a few other graphs  ...  The number of switching isomorphism classes of complete graphs grows super-exponentially [4] .  ... 
doi:10.26493/1855-3974.1605.43f fatcat:xzcosbofqrfvvej3ksdrumemfm

On graphs with maximum size in their switching classes

Sergiy Kozerenko
2015 Commentationes Mathematicae Universitatis Carolinae  
In 2001 in his PhD thesis [4] , Hage posed two related problems: (1) Characterize the maximum (or minimum) size graphs in switching classes. (2) Characterize those switching classes that have a unique  ...  Therefore, if G is unique s-maximal graph in its s-class, then G ≃ K n,n or G ≃ K n,n+1 or G is pancyclic. Definition 2 . 1 . 21 Let G be a graph and U ⊂ V (G).  ... 
doi:10.14712/1213-7243.015.105 fatcat:deelbsr3nbeo3l7p6ji3jwwfli

The Dimension of the Negative Cycle Vectors of Signed Graphs [article]

Alex Schaefer, Thomas Zaslavsky
2017 arXiv   pre-print
Let SpecC(Γ) denote the list of lengths of cycles in Γ. We equip each signed graph with a vector whose entries are the numbers of negative k-cycles for k∈SpecC(Γ).  ...  Using matchings with a strong permutability property, we provide lower bounds on the dimension of this space; in particular, we show for complete graphs, complete bipartite graphs, and a few other graphs  ...  The vectors for K 3 are The number of switching isomorphism classes of complete graphs grows superexponentially [2] .  ... 
arXiv:1706.09041v1 fatcat:iwmaippnxbdx7myazpnhhy7czu

Bipancyclic Subgraphs in Random Bipartite Graphs

Yilun Shang
2013 International Journal of Open Problems in Computer Science and Mathematics  
This result is tight in two ways. First, the range of p is essentially best possible. Second, the proportion 1/2 of edges cannot be reduced.  ...  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  ...  Analogously, a graph on n vertices is called pancyclic if it contains cycles of all length t for 3 ≤ t ≤ n. Clearly, (bi)pancyclic graphs are Hamiltonian but the converse is not true in general.  ... 
doi:10.12816/0006180 fatcat:dplppllb3bfuva6vpv5svpkcve

Bipancyclic subgraphs in random bipartite graphs [article]

Yilun Shang
2012 arXiv   pre-print
This result is tight in two ways. First, the range of p is essentially best possible. Second, the proportion 1/2 of edges cannot be reduced.  ...  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  ...  Analogously, a graph on n vertices is called pancyclic if it contains cycles of all length t for 3 ≤ t ≤ n. Clearly, (bi)pancyclic graphs are Hamiltonian but the converse is not true in general.  ... 
arXiv:1211.6766v2 fatcat:tqd4szf5pzefdmql43tuvfdr6e

Conditions for a Bigraph to be Super-Cyclic

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo, Dara Zirlin
2021 Electronic Journal of Combinatorics  
We present two natural necessary conditions for a hypergraph to be super-pancyclic, and show that in several classes of hypergraphs these necessary conditions are also sufficient.  ...  In particular, they are sufficient for every hypergraph $\mathcal H$ with $ \delta(\mathcal H)\geqslant \max\{|V(\mathcal H)|, \frac{|E(\mathcal H)|+10}{4}\}$.  ...  Super-pancyclic hypergraphs and super-cyclic bigraphs Recall that an n-vertex graph is pancyclic if it contains a cycle of length for every 3 n.  ... 
doi:10.37236/9683 fatcat:o26eqppzfracpabfzwax7eciju

Graph classes characterized both by forbidden subgraphs and degree sequences

Michael D. Barrus, Mohit Kumbhat, Stephen G. Hartke
2007 Journal of Graph Theory  
We say that F is a degree-sequence-forcing set if, for each graph G in the class C of F-free graphs, every realization of the degree sequence of G is also in C.  ...  [7] characterized all pairs of connected graphs {A, B} such that any 3-connected {A, B}-free graph is pancyclic.  ...  In this paper, we address the question of which classes of graphs can be characterized both in terms of a small collection of forbidden subgraphs, and in terms of their degree sequences.  ... 
doi:10.1002/jgt.20270 fatcat:e7ricnwhj5hcbndfacc6j46kiy
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