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Star-factorization of symmetric complete bipartite multi-digraphs

Kazuhiko Ushio
2000 Discrete Mathematics  
We show that a necessary and su cient condition for the existence 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  ... 
doi:10.1016/s0012-365x(99)00321-0 fatcat:wfzkpeguqbfp3ihtjjsez3wc24

Ĉk-factorization of symmetric complete bipartite and tripartite multi-digraphs

Kazuhiko Ushio, Yoshikazu Ohtsubo
2000 Discrete Mathematics  
We show that a necessary and su cient condition for the existence 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.  ... 
doi:10.1016/s0012-365x(00)00104-7 fatcat:sa3gpaul4rhjthghxbnfb75ooi

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 =  ... 

Evenly partite star-factorization of symmetric complete tripartite multi-digraphs

Kazuhiko Ushio
2002 Electronic Notes in Discrete Mathematics  
,nm denote the 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  ... 
doi:10.1016/s1571-0653(04)00106-4 fatcat:4dyvbajaenbr7p7kid7ev7n3ne

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?  ... 

Ǩp,q-factorization of symmetric complete tripartite digraphs

Kazuhiko Ushio, Yoshikazu Ohtsubo
2001 Discrete Mathematics  
Let K * n 1 ;n 2 ;n 3 denote the 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.  ... 
doi:10.1016/s0012-365x(00)00339-3 fatcat:4lzdx4i3xrd7tpwrnw7jzgahsm

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 —  ... 

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  ... 

Completing partial packings of bipartite graphs

Zoltán Füredi, Ago-Erik Riet, Mykhaylo Tyomkyn
2011 Journal of combinatorial theory. Series A  
Let K n and K m,n denote the 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 .  ... 
doi:10.1016/j.jcta.2011.06.009 fatcat:siy7s4akdbcvvmem6nkikqnoeu

Optimal Assignments with Supervisions [article]

Adi Niv, Marie Maccaig, Sergei Sergeev
2019 arXiv   pre-print
We also develop an application 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 .  ... 
arXiv:1807.00512v2 fatcat:ek3i4ytkafesdmyg7bmhvvwola

Optimal assignments with supervisions

Adi Niv, Marie MacCaig, Sergeĭ Sergeev
2020 Linear Algebra and its Applications  
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 .  ...  These can also be viewed as a perfect k-bipartite graph, or specific versions of a perfect star/path/disjoint-k-bipartite graph.  ... 
doi:10.1016/j.laa.2020.02.032 fatcat:h6eifcq765bkrpbop2aftk755e

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.  ... 
doi:10.1016/s0012-365x(00)00198-9 fatcat:pvoli2nzdrc6fjmljo5e2gmmky

Families of line-graphs and their quantization [article]

Prot Pakonski, Karol Zyczkowski
2002 arXiv   pre-print
We show that the non-zero eigenvalues 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 .  ... 
arXiv:nlin/0110043v2 fatcat:vfn5kdacevbxno4g7com64zkg4

Tree containment and degree conditions [article]

Maya Stein
2020 arXiv   pre-print
We survey results and open problems relating degree conditions with tree containment in graphs, random graphs, 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.  ... 
arXiv:1912.04004v2 fatcat:tgw5raavandr3bkfamqlt7ers4

Master index to volumes 271-280

2004 Discrete Mathematics  
Rivera-Campo, On a tree graph defined by a set 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.  ... 
doi:10.1016/s0012-365x(04)00088-3 fatcat:32levbgcczbvdi3ing75aqjdyy
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