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Star-factorization of symmetric complete bipartite multi-digraphs

2000
*
Discrete Mathematics
*

We show that a necessary and su cient condition for the existence

doi:10.1016/s0012-365x(99)00321-0
fatcat:wfzkpeguqbfp3ihtjjsez3wc24
*of*an S k -*factorization**of*the*symmetric**complete**bipartite**multi*-*digraph*K * m; n is m = n ≡ 0 (mod k(k − 1)=d), where d = ( ; k − 1) ... Introduction The*symmetric**complete**bipartite**multi*-*digraph*K * m; n is the*symmetric**complete**bipartite**digraph*K * m; n in which every arc is taken times. ... Let K n1;n2 , K * n1;n2 , K n1;n2;n3 , K * n1;n2;n3 , and K * n1;n2;:::; nm denote the*complete**bipartite*graph, the*symmetric**complete**bipartite**digraph*, the*complete*tripartite graph, the*symmetric**complete*...##
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Ĉk-factorization of symmetric complete bipartite and tripartite multi-digraphs

2000
*
Discrete Mathematics
*

We show that a necessary and su cient condition for the existence

doi:10.1016/s0012-365x(00)00104-7
fatcat:sa3gpaul4rhjthghxbnfb75ooi
*of*aĈ k -*factorization**of*the*symmetric**complete**bipartite**multi*-*digraph*K * n 1 ; n 2 is (i) k ≡ 0 (mod 2) and (ii) n1 = n2 ≡ 0 (mod k ... We also show that a necessary and su cient condition for the existence*of*aĈ kfactorization*of*the*symmetric**complete*tripartite*multi*-*digraph*K * n 1 ; n 2 ; n 3 is (i) k ≡ 0 (mod 2) and (ii) n1 = n2 ... Introduction The*symmetric**complete**bipartite**multi*-*digraph*K * n1; n2 is the*symmetric**complete**bipartite**digraph*K * n1; n2 in which every arcs are taken times. ...##
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Page 5327 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

k =3 and nm, =n2 =n; =0 (mod k(k —1)/2) for k > 5.”
2000h:05176 05C70
Ushio, Kazuhiko (J-KINKS-IE; Higashi-Osaka)
Bigraph-

*factorization**of**symmetric**complete**bipartite**multi*-*digraphs*. ... Summary: “We show that a necessary and sufficient condition for the existence*of*a K,,-*factorization**of*the*symmetric**complete**bipartite**multi*-*digraph*1K, ,, is (i) m =n =0 (mod p) for p=q and (ii) m = ...##
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Evenly partite star-factorization of symmetric complete tripartite multi-digraphs

2002
*
Electronic Notes in Discrete Mathematics
*

,nm denote the

doi:10.1016/s1571-0653(04)00106-4
fatcat:4dyvbajaenbr7p7kid7ev7n3ne
*complete**bipartite*graph, the*symmetric**complete**bipartite**digraph*, the*symmetric**complete*tripartite*digraph*, and the*symmetric**complete*multipartite*digraph*, respectively. ... We show that necessary and sufficient conditions for the existence*of*a semi-evenly partite*star*-*factorization**of*the*symmetric**complete*tripartite*digraph*K~I,n2,n3 are (i) k is even, k 2 4 and (ii) ... Introduction Let K~l ,n2,n3 denote the*symmetric**complete*tripartite*digraph*with partite sets VI, V 2 , V3*of*nl, n2, n3 vertices each, and let Eh denote the semi-evenly partite directed*star*from a center-vertex ...##
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Page 1724 of Mathematical Reviews Vol. , Issue 2004c
[page]

2004
*
Mathematical Reviews
*

*bipartite*

*multi*-

*digraphs*. ... . the existence

*of*a P3-

*factorization*

*of*the

*symmetric*

*complete** myn? ...

##
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Ǩp,q-factorization of symmetric complete tripartite digraphs

2001
*
Discrete Mathematics
*

Let K * n 1 ;n 2 ;n 3 denote the

doi:10.1016/s0012-365x(00)00339-3
fatcat:4lzdx4i3xrd7tpwrnw7jzgahsm
*symmetric**complete*tripartite*digraph*with partite sets V1; V2; V3*of*n1; n2; n3 vertices each, and letKp;q denote the*complete**bipartite**digraph*in which all arcs are ... We show that a necessary condition for the existence*of*aKp;q-*factorization**of*K * n 1 ;n 2 ;n 3 is n1 = n2 = n3 ≡ 0 (mod dp q (p + q )) for p + q ≡ 1; 2 (mod 3) and n1 = n2 = n3 ≡ 0 (mod dp q (p + q ) ... Applying Theorem 3, K * n; n; n has aK p; q -*factorization*. Note: The case for p +q ≡ 0 (mod 3), n 1 =n 2 =n 3 =sdp q (p +q )=3, s ≡ 1; 5 (mod 6), s¿5 is open. ...##
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Page 7631 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

{For the entire collection see MR 2000k:05009. }
2000k:05224 05C70
Ushio, Kazuhiko (J-KINKS-IE; Higashi-Osaka)

*Star*-*factorization**of**symmetric**complete**bipartite**multi*-*digraphs*. ... Summary: “We show that a necessary and sufficient condition for the existence*of*an S,-*factorization**of*the*symmetric**complete*bi- partite*multi*-*digraph*1K, , ism =n =0 (mod k(k —1)/d), where d =(4,k — ...##
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Page 49 of Mathematical Reviews Vol. , Issue 80A
[page]

1980
*
Mathematical Reviews
*

In this paper r,(A,B) is computed for the pairs A/B equal to path/cycle, path/

*star*, path/*complete*graph, and*star*/*complete*graph. ... The Ramsey number R(G,,G,)*of*a pair*of*directed graphs is the smallest n such that for every {1,2} coloring*of*the edges*of*the*complete*directed*symmetric*graph on n points there is an i-chro- matic ...##
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Completing partial packings of bipartite graphs

2011
*
Journal of combinatorial theory. Series A
*

Let K n and K m,n denote the

doi:10.1016/j.jcta.2011.06.009
fatcat:siy7s4akdbcvvmem6nkikqnoeu
*complete*graph on n vertices and the*complete**bipartite*graph with*bipartition*classes*of*size m and n. The graph K 1,k is also called a k-*star*. ... Define a*multi*-k-graph (k-uniform hypergraph with several edges on the same set*of*vertices allowed) called M as follows: for every*star**of*C there is a k-edge containing precisely the leaves*of*the*star*... By Theorem 5, if n is sufficiently large, there is a*complete*packing P*of*K n with copies*of*H . ...##
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Optimal Assignments with Supervisions
[article]

2019
*
arXiv
*
pre-print

We also develop an application

arXiv:1807.00512v2
fatcat:ek3i4ytkafesdmyg7bmhvvwola
*of*this theorem to optimal assignments with supervisions. ... In this paper we provide a new graph theoretic proof*of*the tropical Jacobi identity, recently obtained in [AGN16]. ... The*complete**bipartite*graph, denoted K m,n is the*bipartite*graph G = ([m], [n], E) : E = {(u, v) : u ∈ [m], v ∈ [n]}. A*star*is the*complete**bipartite*graph K 1,k , denoted as ST k . ...##
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Optimal assignments with supervisions

2020
*
Linear Algebra and its Applications
*

The

doi:10.1016/j.laa.2020.02.032
fatcat:h6eifcq765bkrpbop2aftk755e
*complete**bipartite*graph, denoted K m,n is the*bipartite*graph G = ([m], [n], E) : E = {(u, v) : u ∈ [m], v ∈ [n]}. A*star*is the*complete**bipartite*graph K 1,k , denoted as ST k . ... These can also be viewed as a perfect k-*bipartite*graph, or specific versions*of*a perfect*star*/path/disjoint-k-*bipartite*graph. ...##
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Index

2000
*
Discrete Mathematics
*

*of*

*symmetric*

*complete*tripartite

*digraphs*(Note) 211 (2000) 281}286 Ushio, K.,

*Star*-

*factorization*

*of*

*symmetric*

*complete*bipar-Verri, M.C., see D. ... Hagita, Toughness and the existence

*of*k-

*factors*. IV 216 (2000) 111}120 Enomoto, H. and T. Tokuda,

*Complete*-

*factors*and f-

*factors*(Note) 220 (2000) 239}242 Enomoto, H., S. Matsunaga and K. ...

##
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Families of line-graphs and their quantization
[article]

2002
*
arXiv
*
pre-print

We show that the non-zero eigenvalues

arXiv:nlin/0110043v2
fatcat:vfn5kdacevbxno4g7com64zkg4
*of*the adjacency matrices are the same for all graphs*of*such a family L^n(G). ... Line-graphs may therefore serve as models to study the semiclassical limit (*of*large matrix size)*of*a quantum dynamics on graphs with fixed classical behaviour. ... These results were observed for families originating from fully connected*digraphs*(de Bruijn),*symmetric*cycles and*bipartite**digraphs**of*the form K 1,M and K 2,M . ...##
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Tree containment and degree conditions
[article]

2020
*
arXiv
*
pre-print

We survey results and open problems relating degree conditions with tree containment in graphs, random graphs,

arXiv:1912.04004v2
fatcat:tgw5raavandr3bkfamqlt7ers4
*digraphs*and hypergraphs, and their applications in Ramsey theory. ... They also note that if we restrict Conjecture 8.4 to*symmetric**digraphs*(a*digraph*is*symmetric*if all its edges are bidirected), then the conjecture becomes equivalent to the Erdős-Sós conjecture (Conjecture ... One can also consider any other (k − 1)-regular graph, for instance the*complete**bipartite*graph K k−1,k−1 , which does not contain the*star*with k edges. ...##
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Master index to volumes 271-280

2004
*
Discrete Mathematics
*

Rivera-Campo, On a tree graph defined by a set

doi:10.1016/s0012-365x(04)00088-3
fatcat:32levbgcczbvdi3ing75aqjdyy
*of*cycles 271 (2003) 303-310 Lichiardopol, N., Concerning two conjectures on the set*of*fixed points*of*a*complete*rotation*of*a Cayley*digraph*280 (2004) ... Liu, Number*of*maximum matchings*of**bipartite*graphs with positive surplus 274 (2004) 311-318 Llad ! o, A. and S.C. ...
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