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Complete bipartite factorisations of Kn,n
2003
Discrete Mathematics
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We continue the study of complete factorisations of complete bipartite graphs of the form Kn;n by factors whose components are copies of Kp;q for given, ÿxed, p ¡ q. ...
This paper sets out a general strategy for showing that these conditions are also su cient for p and q coprime and odd extending work of earlier papers where the case p = 1 was solved. ...
Acknowledgements The author wishes to record his thanks to the referees for their careful reading of the manuscript and for their helpful suggestions in its revision. ...
doi:10.1016/s0012-365x(02)00819-1
fatcat:dddb5azlpnhfta45umsndqccvu
Complete bipartite factorisations by complete bipartite graphs
1997
Discrete Mathematics
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We study complete Kp,q-factorisations of Kin, n, Simple necessary conditions are found and we conjecture that these conditions are also sufficient. ...
A general construction is given to find infinite families of factorisations proving the conjecture in many cases. The conjecture is proved for Kl,q-factorisations of Kn, n except for q = 4k + 1. ...
The vertex (respectively edge) set of a graph G will be denoted V(G) (respectively E(G)). Km,n will denote a complete bipartite graph on sets of size m and n. ...
doi:10.1016/s0012-365x(97)00248-3
fatcat:onzhpz5bmjg3fj76aoqnc36aui
Page 52 of Mathematical Reviews Vol. , Issue 99a
[page]
1991
Mathematical Reviews
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Here, the au- thors prove that if G is a simple connected graph and k > 2 is an integer such that (i) kn is even, (ii) n > 9k — 1 —4)/2(k — 1)? ...
We present a complete solution of this problem for the case D > 4. ...
Page 3898 of Mathematical Reviews Vol. , Issue 81J
[page]
1981
Mathematical Reviews
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Robinson (Newcastle)
Quinn, Stephen J. 81j:05072 Factorisation of complete bipartite graphs into two isomorphic subgraphs.
Combinatorial mathematics, VI (Proc. Sixth Austral. Conf., Univ. ...
These two isomorphic subgraphs are called factors in the factorisation, and if G= Kn» ...
A sufficient condition for graphs to be fractional (k,m)-deleted graphs
2011
Applied Mathematics Letters
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This result is best possible in some sense, and it is an extension of Zhou's previous results. ...
Let h : where H is any subgraph of G with m edges. In this paper, we use a binding number to obtain a sufficient condition for a graph to be a fractional (k, m)deleted graph. ...
graph is bipartite). ...
doi:10.1016/j.aml.2011.03.041
fatcat:ewgatz7y4fb4nmkluiqud4zn6e
Hamiltonian cycles and 1-factors in 5-regular graphs
[article]
2021
arXiv
pre-print
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of 1-factorisations each containing at least one perfect pair. ...
., 10 }, there exist infinitely many 5-regular graphs of genus g containing a 1-factorisation with exactly k pairs of 1-factors that are perfect, i.e. form a hamiltonian cycle. ...
Zamfirescu's research is supported by a Postdoctoral Fellowship of the Research Foundation Flanders (FWO). ...
arXiv:2008.03173v2
fatcat:5cyupj3qcreenc7y6hbss4nowe
Tree amalgamations and quasi-isometries
[article]
2018
arXiv
pre-print
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of their terminal factorisations. ...
In the end, we discuss the impact of our results to a question of Woess. ...
. * G 1 n * . . . * G kn n . ...
arXiv:1812.04987v1
fatcat:aqrbueoasvha5jf22tl2mafqam
Entanglement content of quantum particle excitations. III. Graph partition functions
2019
Journal of Mathematical Physics
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We consider two measures of entanglement, the logarithmic negativity and the entanglement entropy, between regions of space in excited states of many-body systems formed by a finite number of particle ...
is given by the entanglement of natural qubit states, representing the uniform distribution of particles in space. ...
Consider the set G k,n of all graphs as follows. They are formed by the 2kn vertices V = {V j,m : j ∈ I k , m ∈ I n , ∈ {l, r}} -two sets, "left" and "right", of kn vertices -and kn edges. ...
doi:10.1063/1.5098892
fatcat:7fgpcgdo35eevg3e7uwpf4tlxq
Regular embeddings of Kn,n where n is an odd prime power
2007
European journal of combinatorics (Print)
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The method involves groups which factorise as a product of two cyclic groups of order n. ...
We show that if n = p e where p is an odd prime and e ≥ 1, then the complete bipartite graph K n,n has p e−1 regular embeddings in orientable surfaces. ...
Our aim is to consider the regular orientable embeddings of the complete bipartite graphs K n,n . ...
doi:10.1016/j.ejc.2005.07.021
fatcat:c25apmk6czhmvfhddekza6j2be
Master index of volumes 181–190
1998
Discrete Mathematics
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Lindner, The Doyen-Wilson theorem for maximum packings of Kn with 4-cycles Fu, H.-L., see B.-L. ...
Halperin, Bipartite subgraphs of integer weighted graphs 181 (1998) 19-29 Alsardary, S.Y. and J. Wojciechowski, The basis number of the powers of the complete graph 188 (1998) 13-25 Amar, D. and O. ...
doi:10.1016/s0012-365x(98)90328-4
fatcat:s2tsivncvfcilf6jlbl4fx24zq
Norms of idempotent Schur multipliers
[article]
2014
arXiv
pre-print
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Many of our arguments are framed in the combinatorial language of bipartite graphs. ...
We also show that the Schur idempotents which keep only the diagonal and superdiagonal of an n x n matrix, or of an n x (n+1) matrix, both have norm 2/(n+1) cot(pi/(n+1)), and we consider the average norm ...
,n,1/2 G q ≥ Kn | 1 q − 1 2 | . ...
arXiv:1302.4849v2
fatcat:e2gmzgduezgtzfi67nqyemkyju
Multicolour Turán problems
2004
Advances in Applied Mathematics
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A simple k-colouring of a multigraph G is a decomposition of the edge multiset as the sum of k simple graphs, called 'colours'. ...
For complete bipartite graphs K r,s with s > (r − 1)! ...
The problem is more challenging for bipartite graphs that contain cycles. In this section we will be concerned with the case of complete bipartite graphs K r,s . ...
doi:10.1016/j.aam.2003.08.005
fatcat:umtvbqkdm5ga3cxpnf2ic3hrsq
Telecloning of qudits via partially entangled states
2016
Quantum Information Processing
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The results presented here are valid for arbitrary numbers of copies of a single input qudit state of any dimension. ...
We study the process of quantum telecloning of d-dimensional pure quantum states using partially entangled pure states as quantum channel. ...
(22) is transformed into the state GXOR P X |ψ P X AC = 1 d d−1 n,m=0 d−1 k=0 c k ω kn |k P |m X ⊗ U −1 nm d−1 j=0 α j |φ j AC , (26) where the systems X and P are factorisable. ...
doi:10.1007/s11128-016-1348-2
fatcat:kztwd3vobjbuhkdwr63gih4suy
A survey on additive and multiplicative decompositions of sumsets and of shifted sets
[chapter]
2009
Combinatorial Number Theory and Additive Group Theory
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The methods involved are of analytic nature such as the large sieve, and of combinatorial nature such as extremal graph theory. ...
In this paper we survey results on sumsets with multiplicative properties and the question if a shifted copy of a multiplicatively defined set can again be multiplicatively defined. ...
A complete bipartite graph K s,t corresponds to disjoint sets of primes A and B of sizes s and t such that all λa i + (1 − λ)b j are also prime. ...
doi:10.1007/978-3-7643-8962-8_16
fatcat:vm7nqjyckjdnpi4wctrn5k3ke4
A SUFFICIENT CONDITION FOR A GRAPH TO BE A FRACTIONAL ( f, n)-CRITICAL GRAPH
2010
Glasgow Mathematical Journal
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Let a, b and n be non-negative integers such that 1 ≤ a ≤ b, and let G be a graph of order p with p ≥ (a+b−1)(a+b−2)+bn−2 https://www.cambridge.org/core/terms. https://doi. ...
graph is bipartite). ...
Suppose |N G (X)| > (k − 1)p + |X| + kn − 1 2k − 1 for every non-empty independent subset X of V (G), and δ(G) > (k − 1)p + 2k + kn − 2 2k − 1 , then G is a fractional (k, n)-critical graph. ...
doi:10.1017/s001708951000011x
fatcat:ykjxrvd2hvha3hf23vw6myrjbq
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