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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. ...##
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Vertex pancyclic graphs

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. ...

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Pancyclic properties of the graph of some 0–1 polyhedra

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*). ...

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

2002
*
Electronic Journal of Combinatorics
*

The directed anti-Oberwolfach problem asks for a 2-factorization (each factor has

doi:10.37236/1633
fatcat:sl7smrkf5fftzhoj2ahtgkuqua
*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. ...##
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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. ...

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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-

doi:10.1016/s0012-365x(04)00280-8
fatcat:gv6egom3pffcjhh2yfx5bvnycq
*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. ...##
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The anti-Oberwolfach solution: pancyclic 2-factorizations of complete graphs

2003
*
Theoretical Computer Science
*

We pose and completely solve the existence of

doi:10.1016/s0304-3975(02)00650-3
fatcat:ibknop4eujdthk4o3js235baye
*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*...##
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The dimension of the negative cycle vectors of a signed graph

2019
*
Ars Mathematica Contemporanea
*

Let SpecC(Γ) denote the list of lengths of cycles

doi:10.26493/1855-3974.1605.43f
fatcat:xzcosbofqrfvvej3ksdrumemfm
*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] . ...##
###
On graphs with maximum size in their switching classes

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). ...

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

2017
*
arXiv
*
pre-print

Let SpecC(Γ) denote the list of lengths of cycles

arXiv:1706.09041v1
fatcat:iwmaippnxbdx7myazpnhhy7czu
*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] . ...##
###
Bipancyclic Subgraphs in Random Bipartite Graphs

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

This result is tight

doi:10.12816/0006180
fatcat:dplppllb3bfuva6vpv5svpkcve
*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. ...##
###
Bipancyclic subgraphs in random bipartite graphs
[article]

2012
*
arXiv
*
pre-print

This result is tight

arXiv:1211.6766v2
fatcat:tqd4szf5pzefdmql43tuvfdr6e
*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. ...##
###
Conditions for a Bigraph to be Super-Cyclic

2021
*
Electronic Journal of Combinatorics
*

We present two natural necessary conditions for a hypergraph to be super-

doi:10.37236/9683
fatcat:o26eqppzfracpabfzwax7eciju
*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. ...##
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Graph classes characterized both by forbidden subgraphs and degree sequences

2007
*
Journal of Graph Theory
*

We say that F is a degree-sequence-forcing set if, for each graph G

doi:10.1002/jgt.20270
fatcat:e7ricnwhj5hcbndfacc6j46kiy
*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. ...
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