A lower bound for the permanents of certain (0,1)-matrices

Voorhoeve, Marc

doi:10.1016/1385-7258(79)90012-x

Cited by 48 publications

(62 citation statements)

References 2 publications

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“…(A perfect-matching or 1-factor is a set of disjoint edges covering all vertices.) This generalizes a result of Voorhoeve [11] for the case k=3, stating that any 3-regular bipartite graph with 2n vertices has at least ( 4 3 ) n perfect matchings. The base in (1) is best possible for any k: let : k be the largest real number such that any k-regular bipartite graph with 2n vertices has at least (: k ) n perfect matchings; then…”

Section: Introductionsupporting

confidence: 59%

See 1 more Smart Citation

Counting 1-Factors in Regular Bipartite Graphs

Schrijver

1998

Journal of Combinatorial Theory, Series B

109

113

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Section: Introductionsupporting

confidence: 59%

“…The result of Voorhoeve [11] for the case k=3 answered a question posed by Erdo s and Re nyi [3]: is there an =>0 such that the permanent of any nonnegative integer n_n matrix with all row and column sums equal to 3 is at least (1+=) n ? So Voorhoeve's result shows that one can take == 1 3 .…”

Section: Introductionmentioning

confidence: 97%

Counting 1-Factors in Regular Bipartite Graphs

Schrijver

1998

Journal of Combinatorial Theory, Series B

109

113

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“…1.8]). This conjecture has been verified for bipartite cubic graphs (see [11,12] and also [10,Chapter 8]) but, beyond this, not much seems to be known about the number of perfect matchings in 2-connected cubic graphs.…”

Section: Introductionmentioning

confidence: 93%

Graphs with independent perfect matchings

Carvalho¹,

Lucchesi²,

Murty

2004

J. Graph Theory

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A graph with at least two vertices is matching covered if it is connected and each edge lies in some perfect matching. A matching covered graph G is extremal if the number of perfect matchings of G is equal to the dimension of the lattice spanned by the set of incidence vectors of perfect matchings of G. We first establish several basic properties of extremal matching covered graphs. In particular, we show that every extremal brick may be obtained by splicing graphs whose underlying simple graphs are odd wheels. Then, using the main theorem proved in [2] and [3], we find all the extremal cubic matching covered graphs.ß

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“…The infimum corresponds to random bipartite graphs G. Theorem 9.13 (Voorhoeve [54] for d = 3 and Schrijver [51] for all d). If G is a d-regular bipartite graph on 2n vertices, then [42] for an exposition.…”

Section: Theorem 99 ([36]mentioning

confidence: 99%