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The linear 3-arboricity of Kn,n and Kn

Hung-Lin Fu, Kuo-Ching Huang, Chih-Hung Yen
2008 Discrete Mathematics  
In this paper, we 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.  ... 
doi:10.1016/j.disc.2007.07.067 fatcat:t6tmklwfhfh3pnwpu5gxc3bfey

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).  ... 

Chordal, interval, and circular-arc product graphs

Tatiana Hartinger
2016 Applicable Analysis and Discrete Mathematics  
A 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.  ... 
doi:10.2298/aadm160913020h fatcat:gj5blxhxbncmba47vpnxldohuq

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.  ... 


2003 Discrete Mathematics  
Selvaraju Decompositions 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.  ... 
doi:10.1016/s0012-365x(02)00779-3 fatcat:c6ruhvugjzazdi7o6mlx4drqrq

Critical properties of bipartite permutation graphs [article]

Bogdan Alecu, Vadim Lozin, Dmitriy Malyshev
2020 arXiv   pre-print
The class 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] .  ... 
arXiv:2010.14467v1 fatcat:4limdlsygvdatfeyksncg3bm2u

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]

Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič
2014 Fields Institute Communications  
Combining the theory 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.  ... 
doi:10.1007/978-1-4939-0781-6_2 fatcat:3zeawbc6lbdzpfomiwkmrxygwa

On the dimension of trees

S. Poljak, A. Pultr
1981 Discrete Mathematics  
It is prov& that for trees (and 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.  ... 
doi:10.1016/0012-365x(81)90064-9 fatcat:aakxkvs3h5ghjpk6rh7bkgsn6y

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.  ... 

Towards an Isomorphism Dichotomy for Hereditary Graph Classes [article]

Pascal Schweitzer
2014 arXiv   pre-print
First, we develop a methodology to show 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.  ... 
arXiv:1411.1977v1 fatcat:4s5nlu54pnfwrdpht47ztm4dri

On the linear (n−1)-arboricity of Kn(m)

Bing Xue, Liancui Zuo
2010 Discrete Applied Mathematics  
In this paper, we obtain the exact value 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.  ... 
doi:10.1016/j.dam.2010.04.013 fatcat:hkpzkj5tbjgpnl4tg6k7zinam4
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