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Star-factorization of symmetric complete bipartite multi-digraphs
2000
Discrete Mathematics
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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
2000
Discrete Mathematics
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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
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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
2002
Electronic Notes in Discrete Mathematics
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,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
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bipartite multi-digraphs. ...
. the existence of a P3-factorization of the symmetric complete
* myn? ...
Ǩp,q-factorization of symmetric complete tripartite digraphs
2001
Discrete Mathematics
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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
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{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
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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
2011
Journal of combinatorial theory. Series A
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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]
2019
arXiv
pre-print
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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
2020
Linear Algebra and its Applications
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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
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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]
2002
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
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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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