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Page 2310 of Mathematical Reviews Vol. , Issue 99d
[page]
1991
Mathematical Reviews
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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
2002
Discrete Applied Mathematics
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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
1984
Journal of combinatorial theory. Series B (Print)
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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
2002
Electronic Journal of Combinatorics
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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
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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
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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
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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
2003
Theoretical Computer Science
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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
2019
Ars Mathematica Contemporanea
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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
2015
Commentationes Mathematicae Universitatis Carolinae
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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]
2017
arXiv
pre-print
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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
2013
International Journal of Open Problems in Computer Science and Mathematics
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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]
2012
arXiv
pre-print
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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
2021
Electronic Journal of Combinatorics
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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
2007
Journal of Graph Theory
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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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