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pro vyhledávání: '"Lane H. Clark"'
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers $r(G,H
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19aefcf6120feec1db2eb08f4e3d3802
Autor:
Lane H. Clark
Publikováno v:
Applicable Analysis and Discrete Mathematics. 3:303-309
Let An(?) denote the sum of the lengths of ascents of a permutation ? of {1, ..., n} chosen uniformly at random. We find the exact expectation and variance and prove a central limit theorem for the An. Identical results hold for the sum of the length
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https://explore.openaire.eu/search/publication?articleId=doi_________::44d3fa60b647884d7e33a276fc243775
https://doi.org/10.2298/aadm0902303c
https://doi.org/10.2298/aadm0902303c
Autor:
Ivan Gutman, Lane H. Clark
Publikováno v:
Journal of Mathematical Chemistry. 43:32-44
We determine conditions for the parameters n and δ, for which the general Randic index R δ is not an acceptable index of branching of n-vertex trees, i.e., for which the n-vertex star and the n-vertex path have not extremal R δ-values among all n-
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https://explore.openaire.eu/search/publication?articleId=doi_________::266a70e1e3a74759e5250d4a5a87bdd6
https://doi.org/10.1007/s10910-006-9177-7
https://doi.org/10.1007/s10910-006-9177-7
Publikováno v:
Discrete Mathematics. 187(1-3):1-17
For a graph G = ( V , E ), by N = A + I , we denote the closed neighborhood matrix of G where A and I are the adjacency matrix of G and identity matrix, respectively. The parity dimension of G , denoted PD( G ), is the dimension of the null space of
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3e9918d9306e92892711a79dd4022cff
Autor:
Frank Gaitan, Lane H. Clark
In the Graph Isomorphism problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G into G'. If yes, then G and G' are said to be isomo
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d6714504e9cf256c91fccd03d5503d1c
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their exp
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::397f880e7e3ebc35bca918fc1de832ee
http://arxiv.org/abs/1201.1842
http://arxiv.org/abs/1201.1842
Autor:
Lane H. Clark, Frank Gaitan
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers $R
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fe7e114eae52e8487040feda93e4fe6f
http://arxiv.org/abs/1103.1345
http://arxiv.org/abs/1103.1345
Autor:
Lane H. Clark
Publikováno v:
Integers. 10
We prove a general theorem about the multiplicity of the entries in certain integer arrays which is best possible in general. As an application we give non-trivial bounds for the multiplicities of several well-known combinatorial arrays including the
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https://explore.openaire.eu/search/publication?articleId=doi_________::551cb61c3ba2701a45240f15f2590b39
https://doi.org/10.1515/integ.2010.014
https://doi.org/10.1515/integ.2010.014
Autor:
Lane H. Clark
Publikováno v:
Journal of Graph Theory. 16:451-458
For a graphb F without isolated vertices, let M(F; n) denote the minimum number of monochromatic copies of F in any 2-coloring of the edges of Kn. Burr and Rosta conjectured that when F has order t, size u, and a automorphisms. Independently, Sidoren
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https://explore.openaire.eu/search/publication?articleId=doi_________::ed035f389fc8a703fd05de386403305d
https://doi.org/10.1002/jgt.3190160506
https://doi.org/10.1002/jgt.3190160506