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G-designs and related designs

Kazuhiko Ushio
1993 Discrete Mathematics  
., G-designs and related designs, Discrete Mathematics 116 (1993) 2999311. This is a survey on the existence of G-designs, bipartite G-designs and multipartite G-designs.  ...  They can be solved by constructing (u, k, 1) K,-designs, (v, k, 1) Sk-designs, (m, n, k, 1) multipartite K,-designs and (m, n, k, 1) multipartite Sk-designs, respectively.  ...  In any case of G-designs, bipartite G-designs and multipartite G-designs, if the design is resolvable then it is also balanced.  ... 
doi:10.1016/0012-365x(93)90408-l fatcat:h5bupkvqnjch5h4fyckipthdnu

On the metric dimension of incidence graphs [article]

Robert F. Bailey
2018 arXiv   pre-print
The metric dimension μ(Γ) is the smallest size of a resolving set for Γ.  ...  We consider the metric dimension of two families of incidence graphs: incidence graphs of symmetric designs, and incidence graphs of symmetric transversal designs (i.e. symmetric nets).  ...  In such a design, it follows that k = λg and v = |B| = λg 2 , so the parameters depend only on λ and g.  ... 
arXiv:1707.02899v2 fatcat:cvds3bpw6rdrraxkvkpqjroodm

Improving spatial resolution in quantum imaging beyond the Rayleigh diffraction limit using multiphoton W entangled states

Jianming Wen, Shengwang Du, Min Xiao
2010 Physics Letters A  
The one used here refers to the ability to resolve two point sources in the object.  ...  The other is the minimum angle between plane waves falling on an aperture that can be resolved and can be interpreted as resolving two point sources at infinity.  ... 
doi:10.1016/j.physleta.2010.07.068 fatcat:yrbrl2v3evcynpwtk4o3odwopm

Anonymous secret sharing schemes

C. Blundo, D.R. Stinson
1997 Discrete Applied Mathematics  
We also discuss constructions for anonymous secret sharing schemes, and apply them to access structures obtained from complete multipartite graphs.  ...  In this paper, we provide lower bounds on the size of the share sets in any (t,w) threshold scheme, and for an infinite class of non-threshold access structures.  ...  Let G =K,,,,,Wz ,_.., WI be a complete multipartite graph on k parts. If there exists a resolvable Steiner system S Theorem 5.3 (Stinson and Vanstone [26]).  ... 
doi:10.1016/s0166-218x(97)89208-6 fatcat:m3gannbofbe4to7wzj5kqcghdy

Investigating the mitochondrial genomic landscape of Arabidopsis thaliana by long-read sequencing

Bansho Masutani, Shin-Ichi Arimura, Shinichi Morishita
2021 PLoS Computational Biology  
The emergence of long-read sequencing technology is expected to yield this landscape; however, many studies aimed to assemble only one representative circular genome, because properly understanding multipartite  ...  For synthetic data, our proposed method reliably detected one variation site out of 9,000-bp synthetic long reads with a 15% sequencing-error rate and produced accurate clustering.  ...  [0, 1] be normalized weights on E, and G 0 = (V 0 , E 0 ) be the PO-HMM from G and w.  ... 
doi:10.1371/journal.pcbi.1008597 pmid:33434206 pmcid:PMC7833223 fatcat:fyagrny45ngdnmplvwmouxc3c4

Index to Volume 1

1980 European journal of combinatorics (Print)  
L. and FDREDI, z., On automorphisms of line-graphs . 341 ESSER, F. and HARARY, F., On the spectrum of a complete multipartite graph 211 FOATA, D., See ANDREWS, G. E.  ...  A., Transversal designs and doubly-resolvable designs 219 FDREDI, Z., See ERDOS, P. L. GARSIA, A.  ... 
doi:10.1016/s0195-6698(80)80042-4 fatcat:3yewjoxynfes7jzuoji6bsal6u

The mitochondrial genome of Globodera ellingtonae is composed of two circles with segregated gene content and differential copy numbers

Wendy S. Phillips, Amanda M. V. Brown, Dana K. Howe, Amy B. Peetz, Vivian C. Blok, Dee R. Denver, Inga A. Zasada
2016 BMC Genomics  
We report on the two circle multipartite mt genome of a newly described cyst nematode, Globodera ellingtonae.  ...  Results: The G. ellingtonae mt genome was found to be comprised of two circles, each larger than any other multipartite circular mt chromosome yet reported, and both were larger than the single mt circle  ...  All mtDNA sequence segments were covered by at least two clones, or more when needed to resolve discrepancies.  ... 
doi:10.1186/s12864-016-3047-x pmid:27595608 pmcid:PMC5011991 fatcat:mkeqn2qxrnexjemzt7oslqshju

Page 8208 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
G. Kirkpatrick [Graphs Combin. 2 (1986), no. 1, 61-66; MR 92j:05139] on vertex- deleted f-factors. As an example, one of the main results is as follows. Suppose G has f;-factors, 1 <i < p, where °?  ...  G.  ... 

The Software for Constructing Trails with Local Restrictions in Graphs

Tatyana Panyukova, Igor Alferov
2013 Open Journal of Discrete Mathematics  
Let's designate as   E G the sets of vertices and edges of graph G correspondingly.  ...  The degree of vertex v let be designated as ; for let the subgraph received of graph G by deleting of one set of vertices and only all edges incident to vertices of this set.Restrictions for paths  ... 
doi:10.4236/ojdm.2013.32017 fatcat:adcrk3uqdvgszmjrulhzf23aey

Antipodal covers of strongly regular graphs

Aleksandar Jurišić
1998 Discrete Mathematics  
Finally, antipodal covers of complete bipartite graphs and their line graphs are characterized in terms of weak resolvable transversal designs which are, in the case of maximal covering index, equivalent  ...  The dual of a resolvable transversal design TD(v, v/r; r) is actually a resolvable transversal design with the same parameters.  ...  ~ is a weak resolvable transversal design WRTD(v, r).  ... 
doi:10.1016/s0012-365x(97)00139-8 fatcat:shuni5ozqffhroi3psagupjgyy

Assorted Musings on Dimension-critical Graphs [article]

Matt Noble
2021 arXiv   pre-print
Define G to be dimension-critical if every proper subgraph of G has dimension less than G. In this article, we determine exactly which complete multipartite graphs are dimension-critical.  ...  For a finite simple graph G, say G is of dimension n, and write (G) = n, if n is the smallest integer such that G can be represented as a unit-distance graph in ℝ^n.  ...  Designating by v one of the vertices of G of degree 7, we have that G \ {v} is isomorphic to W 6 .  ... 
arXiv:2106.05333v1 fatcat:7l7uvkvgnbdlhdndupnn655t3m

Examining the Heterogeneous Genome Content of Multipartite Viruses BMV and CCMV by Native Mass Spectrometry

Michiel van de Waterbeemd, Joost Snijder, Irina B. Tsvetkova, Bogdan G. Dragnea, Jeroen J. Cornelissen, Albert J. R. Heck
2016 Journal of the American Society for Mass Spectrometry  
Despite their challenging size and heterogeneity, we obtained native mass spectra with resolved series of charge states for both BMV and CCMV, demonstrating that native MS of endogenous multipartite virions  ...  However, the success rate of native MS analysis, particularly in heterogeneous mega-Dalton (MDa) protein complexes, still strongly depends on careful instrument modification.  ...  A more clearly resolved series of charge states is detected. Additionally, at least one additional poorly resolved series of peaks becomes visible distinct particles that were resolved.  ... 
doi:10.1007/s13361-016-1348-6 pmid:26926442 pmcid:PMC4869746 fatcat:x5s5wgblaffo5bzftg5egzdqka

A note on uniformly resolvable decompositions of K v and K v -I into 2-stars and 4-cycles

Salvatore Milici
2013 The Australasian Journal of Combinatorics  
In this paper we consider the uniformly resolvable decomposition of the complete graph K v , or the complete graph minus a 1-factor K v − I, into two graphs such that each resolution class contains only  ...  A (resolvable) H-decomposition of the complete multipartite graph with u parts each of size g is known as a (resolvable) group divisible design H-(R)GDD of type g u , the parts of size g are called the  ...  When H = {K 1,2 , C 4 } a (K 1,2 , C 4 )-URGDD(r, s) of type g u is a uniformly resolvable decomposition of complete multipartite graph with u parts each of size g into r classes consisting entirely of  ... 
dblp:journals/ajc/Milici13 fatcat:zhmfkxctznbkxkp6l3voynmf5a

Page 802 of Mathematical Reviews Vol. 58, Issue 2 [page]

1979 Mathematical Reviews  
Beginning with several explicit examples, including one associated with resolvable designs, the author first studies partition coverings of graphs.  ...  Here K,, is the “star” graph of one vertex adjacent to b others, mG is m disjoint copies of G, and K, is the complete graph on p mutually adjacent vertices.  ... 

Resolvable 4-cycle group divisible designs with two associate classes: Part size even

Elizabeth J. Billington, C.A. Rodger
2008 Discrete Mathematics  
Let 1 K a denote the graph on a vertices with 1 edges between every pair of vertices. Take p copies of this graph 1 K a , and join each pair of vertices in different copies with 2 edges.  ...  The resulting graph is denoted by K(a, p; 1 , 2 ), a graph that was of particular interest to Bose and Shimamoto in their study of group divisible designs with two associate classes.  ...  Such decompositions are known as C z group divisible designs with two associate classes, following the notation of Bose and Shimamoto who considered the existence problem for K z group divisible designs  ... 
doi:10.1016/j.disc.2006.11.043 fatcat:5yzugnduzrgvtgf4wqvdbziuzm
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