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The linear 3-arboricity of Kn,n and Kn
2008
Discrete Mathematics
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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
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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
2016
Applicable Analysis and Discrete Mathematics
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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
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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
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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. ...
Contents
2003
Discrete Mathematics
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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]
2020
arXiv
pre-print
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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
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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
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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
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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
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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
1981
Discrete Mathematics
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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
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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]
2014
arXiv
pre-print
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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)
2010
Discrete Applied Mathematics
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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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