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Page 4781 of Mathematical Reviews Vol. , Issue 98H [page]

1998 Mathematical Reviews  
{For the entire collection see MR 98f:05001.} 98h:05153 05C70 Wang, Hong |Wang, Hong*| (1-NORL; New Orleans, LA) Packing two bipartite graphs into a complete bipartite graph. (English summary) J.  ...  In the paper it is proved that any two compatible C,-free bipartite graphs of order n together with at most 2n —2 edges can be packed into a complete bipartite graph of order at most n + 1, unless one  ... 

Page 2905 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
Summary: “We give explicit results for the numbers of node- disjoint decompositions of complete graphs and complete bipartite graphs into subgraphs which are complete bipartite graphs.  ...  Augustine) Decemposition of complete graphs and complete bipartite graphs into complete bipartite factors. (English summary) J. Math. Sci. (Calcutta) 11 (2000), no. 1, 29-33.  ... 

Page 7343 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
We consider the decomposition of the edges of S° into complete bipartite graphs, and obtain the following results.  ...  is called a minimum complete bipartite decomposition of S°, and a complete bipartite decomposition of S” is said to be trivial if it consists of either m maximal stars with respective centers a), a, ,  ... 

Page 2779 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
It is proved that any pair of compatible trees of order n can be packed into a complete bipartite graph of order n+ 1.  ...  s and 1, respectively.” 97e:05161 05C70 Wang, Hong [Wang, Hong*] (NZ-MASS; Palmerston North) Packing two forests into a bipartite graph.  ... 

The P k Partition Problem and Related Problems in Bipartite Graphs [chapter]

Jérôme Monnot, Sophie Toulouse
2007 Lecture Notes in Computer Science  
Finally, we propose a 3/2-approximation for Min3-PathPartition in general graphs within O(nm + n 2 log n) time and a 1/3 (resp., 1/2)-approximation for MaxWP3Packing in general (resp., bipartite) graphs  ...  in bipartite graphs of maximum degree 3.  ...  For any k ≥ 3, there is a constant ε k > 0, such that ∀G = (V, E) instance of MaxP k Packing (resp., MaxInducedP k Packing) where G is a bipartite graph of maximum degree 3, it is NP-complete to decide  ... 
doi:10.1007/978-3-540-69507-3_36 fatcat:x3qfgf2hifaddkfx7gzn2u53lu

The path partition problem and related problems in bipartite graphs

Jérôme Monnot, Sophie Toulouse
2007 Operations Research Letters  
We prove that it is NP-complete to decide whether a bipartite graph of maximum degree three on nk vertices can be partitioned into n paths of length k.  ...  In [13] , Kirkpatrick and Hell give a necessary and sufficient condition for the NP-completeness of the partition into isomorphic subgraphs problem in general graphs.  ...  Then, we prove that, in bipartite graphs of maximum degree 3, MaxP k Packing and MaxInducedP k Packing do not have a PTAS.  ... 
doi:10.1016/j.orl.2006.12.004 fatcat:xqvtr4qnirhcffwypt35b3ca7e

Page 4036 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
Summary: “Let K,,,,, be a complete bipartite graph with two par- tite sets having m and n vertices, respectively.  ...  The purpose of this paper is to study the tight planar packing of two trees: Is it possible to pack two trees of n vertices, none of them equal to a star, into a planar graph of n vertices?  ... 

A note on packing trees into complete bipartite graphs and on fishburn's conjecture

Y. Caro, Y. Rodity
1990 Discrete Mathematics  
. , T,} can be packed into the complete bipartite graph K,_"n,z (n even) for f = 0.3n.  ...  Hobbs, Bourgeois and Kasiraj [4] conjectured that any sequence of trees (c-1 T3, * * * 3 T,} can be packed into the complete bipartite graph Kn--l,n,Z.  ...  . , T,} can be packed into the complete graph K,,. (For references about the known results one may look at [5] ).  ... 
doi:10.1016/0012-365x(90)90209-z fatcat:o33wvmxlkja2tkwyjq2gi7n6ni

Page 6607 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Summary: “Let {72,---,7,} be a sequence of trees, where 7; has i vertices. We show that if ¢ < 0.79n, then the sequence can be packed into the complete bipartite graph K,,_ | »/2 (resp.  ...  ceptions) satisfying conditions on their sizes, the degrees of their vertices, and the orders of their components, can be packed into the complete graph of order n.  ... 

Page 725 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
Summary: “A complete bipartite graph without one edge, Ky», 98b:05082 is called an almost complete bipartite graph.  ...  A graph Ky, 12m+1 that can be decomposed into two isomorphic factors with a given diameter d is called d-isodecomposable. We prove that Kon, 12m+!  ... 

Some results on triangle partitions [article]

Ton Kloks, Sheung-Hung Poon
2011 arXiv   pre-print
We show that there is an efficient algorithm for C_4-packing on bipartite permutation graphs and we show that C_4-packing on bipartite graphs is NP-complete.  ...  We show that there exist efficient algorithms for the triangle packing problem in colored permutation graphs, complete multipartite graphs, distance-hereditary graphs, k-modular permutation graphs and  ...  In this section we show that the C 4 -packing problem is NP-complete for general bipartite graphs. Theorem 8. C 4 -Packing on bipartite graphs is NP-complete. Proof.  ... 
arXiv:1104.3919v1 fatcat:d3jyf6guongcnp5tkr25svgkzq

Completing Partial Packings of Bipartite Graphs [article]

Zoltán Füredi, Ago-Erik Riet, Mykhaylo Tyomkyn
2010 arXiv   pre-print
Given a bipartite graph H and an integer n, let f(n;H) be the smallest integer such that, any set of edge disjoint copies of H on n vertices, can be extended to an H-design on at most n+f(n;H) vertices  ...  This settles a long-standing open problem.  ...  ., n} into subsets of size about n 0 each and such that each complete bipartite graph (X, Y ) induced on two partition classes X ⊂ {1, ..., m} and Y ⊂ {1, ..., n} is H-divisible.  ... 
arXiv:1007.4287v3 fatcat:yyz257hapbc33gfdi4jppnmd2y

Many disjoint triangles in co-triangle-free graphs [article]

Mykhaylo Tyomkyn
2020 arXiv   pre-print
We also prove a corresponding stability theorem, that all large graphs attaining the above bound are close to being bipartite.  ...  We prove that any n-vertex graph whose complement is triangle-free contains n^2/12-o(n^2) edge-disjoint triangles. This is tight for the disjoint union of two cliques of order n/2.  ...  Equivalently, G is co-bipartite if V (G) is spanned by a disjoint union of two cliques; clearly, co-bipartite graphs are co-triangle-free.  ... 
arXiv:2001.00763v2 fatcat:5wm6wn7slvhvhegqv36alyonby

Coupled-Tasks in Presence of Bipartite Compatibilities Graphs [chapter]

Benoit Darties, Gilles Simonin, Rodolphe Giroudeau, Jean-Claude König
2014 Lecture Notes in Computer Science  
We study several problems in the framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain, . . .).  ...  complete 1-stage bipartite|C max where the compatibility graph is a complete bipartite G=(X,Y), and all the tasks from Y have the same α(y). are approximable to a factor 1 + (1−ρ) 3 .Proof 1.  ...  each item can be packed into some bins only.  ... 
doi:10.1007/978-3-319-09174-7_14 fatcat:hysdy7ruknac5fob2oyafbnrkm

Packing trees in complete bipartite graphs

Jieyan Wang
2019 Discussiones Mathematicae Graph Theory  
We prove that for any tree T of order n, there is a 4-packing of T in a complete bipartite graph of order at most n + 12.  ...  An embedding of a graph H in a graph G is an injection (i.e., a oneto-one function) σ from the vertices of H to the vertices of G such that σ are edge disjoint.  ...  Packing Trees in Complete Bipartite Graphs 13  ... 
doi:10.7151/dmgt.2252 fatcat:enya2wvybnfyrjqljtqmcfvmcy
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