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The linear 3-arboricity of Kn,n and Kn

2008
*
Discrete Mathematics
*

In this paper, we

doi:10.1016/j.disc.2007.07.067
fatcat:t6tmklwfhfh3pnwpu5gxc3bfey
*completely*determine la k (G) when G is a balanced*complete**bipartite**graph*K n,n or a*complete**graph*K n , and k = 3. ... A linear k-*forest*is a*forest*whose components are paths*of*length at most k. The linear k-arboricity*of*a*graph*G, denoted by la k (G), is the least number*of*linear k-*forests*needed to decompose G. ... Acknowledgment The authors thank the referees for many helpful comments which led to a better version*of*this paper. ...##
###
Page 3276 of Mathematical Reviews Vol. , Issue 96f
[page]

1996
*
Mathematical Reviews
*

decompositions

*of**complete*symmetric digraphs*into*the four oriented quadrilaterals. ... An*isomorphic*decomposition*of*a*complete**graph*. (Bulgarian. English, Russian and Bulgarian summaries) Ann. Inst. Archit. Génie Civil Sofia Fasc. II Math. 37 (1993/94), 69-79 (1995). ...##
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Chordal, interval, and circular-arc product graphs

2016
*
Applicable Analysis and Discrete Mathematics
*

A

doi:10.2298/aadm160913020h
fatcat:gj5blxhxbncmba47vpnxldohuq
*graph*G is*bipartite*if its vertex set can be partitioned*into*two independent sets, and co-*bipartite*if it is the complement*of*a*bipartite**graph*. ... Thus, all components*of*one*of*the*factors*must be*complete*. ...##
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Page 5362 of Mathematical Reviews Vol. , Issue 92j
[page]

1992
*
Mathematical Reviews
*

Joseph Straight (1-SUNYF)
92j:05140 05C70 05E30 Michael, T.S. (1-USNA) The decomposition

*of*the*complete**graph**into*three*isomorphic*strongly regular*graphs*. ... The Oberwol- fach problem OP(a), a2,---,@s;Kn,n) for the*bipartite**graph*Ky,» is to determine whether E(K,,,) can be partitioned*into*subgraphs each*of*which is*isomorphic*to Cg, ,,.....a,. ...##
###
Page 763 of Mathematical Reviews Vol. 51, Issue 3
[page]

1976
*
Mathematical Reviews
*

Let G,,(d) be the
smallest cardinal number n such that the

*complete**graph*K, can be decomposed*into*m*isomorphic**factors*with a diameter d. ... Sachs (Iimenau) Kotzig, Anton; Rosa, Alexander 5410 Decomposition*of**complete**graphs**into**isomorphic**factors*with a given diameter. Bull. London Math. Soc. 7 (1975), 51-57. ...##
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Contents

2003
*
Discrete Mathematics
*

Selvaraju
Decompositions

doi:10.1016/s0012-365x(02)00779-3
fatcat:c6ruhvugjzazdi7o6mlx4drqrq
*of**complete**graphs*and*complete**bipartite**graphs**into**isomorphic*supersubdivision*graphs*137 S. Wang and J. Hao The extreme set condition*of*a*graph*151 J. Wu, J. ... CostaLabelings*of*Lee and Hamming spaces 119T.A. McKeeChordal*bipartite*, strongly chordal, and strongly chordal*bipartite**graphs*231 Partitioning Boolean lattices*into*antichains 45 M. ...##
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Critical properties of bipartite permutation graphs
[article]

2020
*
arXiv
*
pre-print

The class

arXiv:2010.14467v1
fatcat:4limdlsygvdatfeyksncg3bm2u
*of**bipartite*permutation*graphs*enjoys many nice and important properties. ... In the present paper we identify critical subclasses*of**bipartite*permutation*graphs**of*various types. ... The induced subgraph*isomorphism*is known to be NP-*complete*in the class*of*linear*forests*, which is a proper subclass*of**bipartite*permutation*graphs*[24] . ...##
###
Page 2275 of Mathematical Reviews Vol. , Issue 85f
[page]

1985
*
Mathematical Reviews
*

Fouquet (Le Mans)
Zelinka, Bohdan (CS-VSST) 85f:05094 Decomposition

*of*an infinite*complete**graph**into**complete**bipartite*subgraphs. (Russian and Czech summaries) Casopis Pést. ... Pollak proved that if a*complete**graph*K,*of*n vertices is decomposed*into*edge-disjoint*complete**bipartite**graphs*, then such a decomposition contains at least n — 1*graphs*and n— 1 is clearly best possible ...##
###
Page 1900 of Mathematical Reviews Vol. , Issue 89D
[page]

1989
*
Mathematical Reviews
*

N. (3-WTRL-B)

*Isomorphic**factorization**of*r-regular*graphs**into*r parts. Discrete Math. 69 (1988), no. 1, 19-34. ... A G-decomposition*of*the*complete**graph*K,, is a partition*of*its edge set*into*subsets such that each subset induces a*graph**isomorphic*to G. ...##
###
Page 2312 of Mathematical Reviews Vol. , Issue 99d
[page]

1991
*
Mathematical Reviews
*

A condition on the

*factor**graphs*is presented which ensures that such components are*isomorphic*. ... A biclique decomposition*of*“K, is a partition*of*the edge set*of*wK, such that each part induces a simple*complete**bipartite**graph*. ...##
###
Cubic Cayley Graphs and Snarks
[chapter]

2014
*
Fields Institute Communications
*

Combining the theory

doi:10.1007/978-1-4939-0781-6_2
fatcat:3zeawbc6lbdzpfomiwkmrxygwa
*of*Cayley maps with the existence*of*certain kinds*of*independent sets*of*vertices in arc-transitive*graphs*, some new partial results are obtained suggesting promising future research ... The well-known conjecture that there are no snarks amongst Cayley*graphs*is considered. ...*isomorphic*to the*complete**graph*K 4 , and it is therefore not near-*bipartite*. ...##
###
On the dimension of trees

1981
*
Discrete Mathematics
*

It is prov& that for trees (and

doi:10.1016/0012-365x(81)90064-9
fatcat:aakxkvs3h5ghjpk6rh7bkgsn6y
*forests*) G one has dim G ~3 log; IG\ (where dim G, the dimension ci G, is the minimum k such that G is embeddable*into*a pfoduct*of*k*complete**graphs*; ICI is the size*of*... Also, for tba*bipartite*dimension lnid G (arising from embeddings*into*P!$ ane has bid G c 8 log; jGI. ... , 4, 31) is the minimum k such that G is*isomorphic*to a full subgraph*of*a KF where K, is a*complete**graph*. A concrete embedding*of*G*into*a K,k is L ailed encoding. ...##
###
Page 5325 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

Summary: “We show that there exists an

*isomorphic**factorization**of*a*complete**bipartite**graph*K (m,n)*into**forests*without isolated vertices if and only if m+n —c divides mn and m,n > c.” 2000h:05161 05C70 ...*graph**into**forest*. ...##
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Towards an Isomorphism Dichotomy for Hereditary Graph Classes
[article]

2014
*
arXiv
*
pre-print

First, we develop a methodology to show

arXiv:1411.1977v1
fatcat:4s5nlu54pnfwrdpht47ztm4dri
*isomorphism**completeness**of*the*isomorphism*problem on*graph*classes by providing a general framework unifying various reduction techniques. ... We show that, given a suitable decomposition functor, the*graph**isomorphism*problem reduces to checking*isomorphism**of*colored prime*graphs*. ... In [24] it is shown that*isomorphism**of*(H 1 , . . . , H t )-free*graphs*is*isomorphism**complete*unless one*of*the forbidden*graphs*is a*forest**of*subdivided stars. ...##
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On the linear (n−1)-arboricity of Kn(m)

2010
*
Discrete Applied Mathematics
*

In this paper, we obtain the exact value

doi:10.1016/j.dam.2010.04.013
fatcat:hkpzkj5tbjgpnl4tg6k7zinam4
*of*the linear (n−1)-arboricity*of*any balanced*complete*n-partite*graph*K n(m) . ... A linear k-*forest**of*an undirected*graph*G is a subgraph*of*G whose components are paths with lengths at most k. ... A spanning subgraph F*of*G is called an H-*factor*if each component*of*F is*isomorphic*to H. ...
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