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On Cyclic Packing of a Tree

2004
*
Graphs and Combinatorics
*

We prove that there exists

doi:10.1007/s00373-004-0583-y
fatcat:gtfakzbqgbcuzfzswp255uirfy
*a**packing**of*bn=2c copies*of**a**tree**of*size dn=2e into K n . Moreover, the proof provides an easy algorithm. ... We use the following terminology:*A**packing**of*k copies*of**a*graph G will be called*a**cyclic**packing**of*G if there exists*a*permutation r*on*V ðGÞ such that the graphs G, rðGÞ, r 2 ðGÞ,..., r kÀ1 ðGÞ are ... Next, because*of*the methods we use, we consider the case*of*the*packing**of*k copies*of**a**tree*.*On*the other hand we obtain something more than the existence*of*the*packing*. ...##
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Page 69 of Mathematical Reviews Vol. , Issue 90A
[page]

1990
*
Mathematical Reviews
*

Finally, there is

*a*report*on*some special*packings*:*a**tree*with an arbitrary graph,*a**tree*with an (n,n — 1) graph,*a**tree*with an (n, n) graph, two (n,n —1) graphs, and two graphs*of*order n. ... In presenting this survey, the author states that he will concen- trate*on*two*packing*problems:*one*concerning dense*packings**of**trees**of*different sizes in K, and the other that*of**packing*two graphs ...##
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PLANAR PACKING OF CYCLES AND UNICYCLIC GRAPHS

2009
*
Demonstratio Mathematica
*

In 2002 Garcia et al. have shown that

doi:10.1515/dema-2009-0402
fatcat:ptqhl4plerg7db7fm77o3azyb4
*a*non-star*tree*T is planary packable into*a*complete graph K n . ... In this paper we show that for any packable cycle C n except*of*the case n = 5 and n = 7 there exists*a*planar*packing*into K n . We also generalize this result to certain classes*of*unicyclic graphs. ...*A**cyclic**packing**of*G is*a**cyclic*permutation*a*: V(G) -> V(G) (so*a*has exactly*one*cycle in its decomposition into cycles).*A*basic result concerning*packing*problem [1] is: THEOREM 1. ...##
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3-D floorplanning using labeled tree and dual sequences

2008
*
Proceedings of the 2008 international symposium on Physical design - ISPD '08
*

We present

doi:10.1145/1353629.1353641
dblp:conf/ispd/WangYZGGC08
fatcat:j3kqlepacfagxdbvlvncibku5i
*a*complete representation for general non-slicing 3-D floorplan or*packing*structures, which uses*a*labeled*tree*and dual sequences. ... For each compact placement, there is*a*corresponding encoding. The number*of*possible*tree*-sequence combinations is (n + 1) n−1 (n!) 2 , the lowest among complete 3-D representations up to date. ... Since the*cyclic*relation problem is resolved, the blocks can be*packed*in*a*sequential order like in 2-D*packing*: Push the blocks*one*by*one*, each to*a*corner until the block cannot be pushed further ...##
###
Planar packing of cycles and unicyclic graphs

2009
*
Demonstratio Mathematica
*

AbstractWe say that

doi:10.1515/dema-2013-0193
fatcat:le7t2lngyven3ooy3ffranggj4
*a*graphIn this paper we show that for any packable cycle ...*A**cyclic**packing**of*G is*a**cyclic*permutation σ : V (G) → V (G) (so σ has exactly*one*cycle in its decomposition into cycles). ... Identifying*a*cycle segment with the equator*of**a*sphere and drawing edges*of*G*on*the northern hemisphere and edges*of*σ(G)*on*the southern hemisphere*one*can see that σ is*a*planar*cyclic**packing*. ...##
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A note on uniquely embeddable forests

2013
*
Discussiones Mathematicae Graph Theory
*

Let F be

doi:10.7151/dmgt.1651
fatcat:pxqaumwspfhwhiab2t4v53vuou
*a*forest*of*order n. It is well known that if F = S n ,*a*star*of*order n, then there exists an embedding*of*F into its complement F . ... In this note we consider*a*problem concerning the uniqueness*of*such an embedding. ... It is easy to see that the*tree*T ′ consists*of*the path joining*a*and b and (maybe)*of*some vertices Since T ′ contains*a*path*on*five vertices, T ′ is not*a*star and by Theorem 2 there is*a**cyclic*...##
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Page 648 of Mathematical Reviews Vol. , Issue 95b
[page]

1995
*
Mathematical Reviews
*

The algorithm is based

*on*the fact that in each*tree*T there exists*a*path*a*such that P(T) = P(T —*a*)+|E|. ...*A*pentagonal*packing*PP(n;t) is*a*family*of*¢ edge-disjoint pen- tagons in the complete graph K,,.*A*pentagonal*packing*is maximal if the complement*of*the union*of*its pentagons is pentagon-free. ...##
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CICLIC: A Tool to Generate Feasible Cyclic Schedules

2006
*
2006 IEEE International Workshop on Factory Communication Systems
*

*A*common way

*of*implementing periodic real-time systems is by means

*of*

*a*

*cyclic*scheduler. ... In this paper,

*a*tool having this function, and named CICLIC is described. The design mechanism is based

*on*algorithms

*of*exhaustive search that use heuristic rules in optimizing searching paths. ... ACKNOWLEDGEMENTS The research for this paper has been sponsored by the Ministry

*of*Science and Technology, through reference project No. DPI20002/01621. ...

##
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Page 1864 of Mathematical Reviews Vol. , Issue 94d
[page]

1994
*
Mathematical Reviews
*

It follows that the Gyarfas

*tree**packing*conjecture and Fishburn’s conjectures hold for*trees*belonging to these families. ... The graph G is*cyclically*m-edge- connected if the size*of*every*cyclic*edge cutset is m or greater. ...##
###
Edge-disjoint packings of graphs

1994
*
Discrete Applied Mathematics
*

In this paper we study two types

doi:10.1016/0166-218x(92)00153-d
fatcat:xjlp5zevqfb5dkq4d62it7f6ja
*of*edge-disjoint*packings**of*graphs. ... The second edge-disjoint*packing*problem concerns partial subgraphs and asks whether*a*given graph H contains at least k copies G as partial subgraphs such that no two such copies*of*G share an edge. ... F-G'lP*packing*problems are also*of*interest when various restrictions such as planarity or being*a**tree*are placed*on*the host graphs. ...##
###
On cyclically embeddable graphs

1999
*
Discussiones Mathematicae Graph Theory
*

An embedding

doi:10.7151/dmgt.1099
fatcat:q3jrvxd6vvhpbfarncjxnwv2i4
*of**a*simple graph G into its complement G is*a*permutation σ*on*V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). ... In this note we consider some families*of*embeddable graphs such that the corresponding permutation is*cyclic*. ... However, if we assume in addition that G is*a**tree*, we have the following result (cf. [11] ). Theorem 4. Let T be*a**tree**of*order n. If T = S n then there exists*a**cyclic*embedding*of*G. ...##
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Page 4118 of Mathematical Reviews Vol. , Issue 98G
[page]

1998
*
Mathematical Reviews
*

And it is

*trees*that this paper focuses*on*; in particular characterizing all those*trees*JT*of*diameter 3 for which there is*a**cyclic*orthogonal double cover*of*K, by T. ... Finally it is shown that for all but 13*of*the 2087*trees*T*on*n = 11, 12 or 13 vertices, there is*a**cyclic*orthogonal double cover*of*K, by 7. ...##
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Page 7188 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

The size

*of*the largest node in any 1|-hinge*tree*is shown to be an invariant*of*the hypergraph, called the de- gree*of**cyclicity*(acyclic hypergraphs have the degree*of**cyclicity*2). ...*A*k-hinge*tree*is*a*set*of*minimal k-hinges that cover all edges*of*H and form*a**tree*with respect to intersection. ...##
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A Round Trip Pattern for Building Decision Trees

2016
*
International Journal of Database Theory and Application
*

This

doi:10.14257/ijdta.2016.9.7.16
fatcat:vg4ofrvzvbbavdv6r2p6usvpgm
*cyclic*pattern starts at creating*a*decision*tree*from initial table altered according to Bayes theorem combined with Pareto values*of*objective functions. ... This paper introduces*a*recursive procedure named round trip pattern for generating decision*trees*based*on*alterable decision tables. ... The overall number*of*processed*packs*is shown in Figure 6 . The*packs*are*cyclically*classified at start*of*each month and the number is increasing as time elapsed. ...##
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On cyclically embeddable (n,n−1)-graphs

2002
*
Discrete Mathematics
*

An embedding

doi:10.1016/s0012-365x(01)00339-9
fatcat:n3pdowolqja4raopwd432wl4hm
*of**a*simple graph G into its complement G is*a*permutation*on*V (G) such that if an edge xy belongs to E(G), then (x) (y) does not belong to E(G). ... We prove that with few exceptions the corresponding permutation may be chosen as*cyclic**one*. ... Then there exists*a**cyclic*embedding*of*G. The general references for these and other*packing*problems are [1, 7, 5] (see also [8] ). ...
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