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Packing cycles in graphs, II

2003
*
Journal of combinatorial theory. Series B (Print)
*

A

doi:10.1016/s0095-8956(02)00007-2
fatcat:dp6xbwnqe5h7hpnxzpvo3mxsta
*graph*G*packs*if for every induced subgraph H of G; the maximum number of vertexdisjoint*cycles**in*H is equal to the minimum number of vertices whose deletion from H results*in*a forest. ... The purpose of this paper is to characterize all*graphs*that*pack*. r ... Let C be a maximum*cycle**packing**in*F : Then we define a*cycle**packing*B*in*ðF \eÞ,P as follows: put B ¼ C if no*cycle**in*C contains e; else, let C be the*cycle**in*C containing e; and let % C be the*cycle*...##
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On maximum cycle packings in polyhedral graphs

English

2014
*
Electronic Journal of Graph Theory and Applications
*

English

This paper addresses upper and lower bounds for the cardinality of a maximum vertex-/edgedisjoint

doi:10.5614/ejgta.2014.2.1.2
fatcat:sokv3td4jvdtvhadvftzxlr6ca
*cycle**packing**in*a polyhedral*graph*G. ... Bounds on the cardinality of such*packings*are provided, that depend on the size, the order or the number of faces of G, respectively. Polyhedral*graphs*are constructed, that attain these bounds. ...*In*this paper, we investigate maximum*cycle**packings**in*polyhedral*graphs*G. ...##
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On the use of augmenting chains in chain packings

1991
*
Discrete Applied Mathematics
*

*In*a

*graph*G=(X,E), we assign to each node u a positive integer b(o)cdc(u), where C&(U) is the degree of v

*in*G. ... We show that the use of augmenting chains fails

*in*general to produce a new short chain

*packing*from an old one, even for bipartite

*graphs*, but that it does do so for the special case of trees. ... Acknowledgement This paper was written while the first author was visiting RUTCOR (Rutgers Center for Operations Research, Rutgers University)

*in*May and June 1988. The support of the U.S. ...

##
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Between Proper and Strong Edge-Colorings of Subcubic Graphs
[chapter]

2020
*
Lecture Notes in Computer Science
*

Our research is motivated by the conjecture proposed

doi:10.1007/978-3-030-48966-3_27
fatcat:7uapml3a6vef3lmflby6kaj57m
*in*a recent paper on S-*packing*edgecolorings (N. Gastineau and O. Togni, On S-*packing*edge-colorings of cubic*graphs*, Discrete Appl. ... We also show that if a*graph*is*in*class I, the number of induced matchings can be decreased by one, hence confirming the conjecture for this class of*graphs*. ... This research has been done*in*the scope of the bilateral project between France and Slovenia, BI-FR/19-20-PROTEUS-001. ...##
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Packing disjoint cycles over vertex cuts

2010
*
Discrete Mathematics
*

For a

doi:10.1016/j.disc.2010.03.009
fatcat:xc53bpltzbedlmrrtbb26fli5q
*graph*G, let ν(G) and ν (G) denote the maximum cardinalities of*packings*of vertexdisjoint and edge-disjoint*cycles*of G, respectively. ... We study the interplay of these two parameters and vertex cuts*in**graphs*. ... Introduction*Packing*vertex-or edge-disjoint*cycles**in**graphs*is a very well-studied and classical*graph*-theoretical problem. ...##
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Packing edge-disjoint cycles in graphs and the cyclomatic number

2010
*
Discrete Mathematics
*

For a

doi:10.1016/j.disc.2009.07.017
fatcat:pq2pth4hxjctfaoqbfefgap4zm
*graph*G let µ(G) denote the cyclomatic number and let ν(G) denote the maximum number of edge-disjoint*cycles*of G. ... We prove that for every k ≥ 0 there is a finite set P (k) such that every 2-connected*graph*G for which µ(G) − ν(G) = k arises by applying a simple extension rule to a*graph**in*P (k). ... For a*cycle**packing*C, the set of edges contained*in*some*cycle**in*C is denoted by E C . ν(G) ≤ µ(G) which holds for every*graph*G. ...##
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Page 5186 of Mathematical Reviews Vol. , Issue 96i
[page]

1996
*
Mathematical Reviews
*

Summary: “A

*cycle**packing**in*a [directed] multigraph is a ver- tex disjoint collection of [directed] elementary*cycles*. ... Summary: “Let G be a connected*graph*on n vertices, and let a, B, y and 6 be edge-disjoint*cycles**in*G such that (i) a, B [resp. y, 6] are vertex-disjoint and (*ii*) ja|+|f| = |y| + |6| = n, where |a| denotes ...##
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Cycle packings of the complete multigraph
[article]

2017
*
arXiv
*
pre-print

While

arXiv:1701.05287v2
fatcat:n7es55rekbax3icil57rdkk3i4
*cycle*decompositions can give rise to*packings*by removing*cycles*from the decomposition,*in*general it is not known when there exists a*packing*of the complete multigraph with*cycles*of various ...*In*this paper we characterise exactly when there exists a*packing*of the complete multigraph with*cycles*of specified lengths m_1,m_2,...,m_τ. ... A*cycle**packing*of a multigraph G is a*packing*P of G such that each submultigraph*in*P is a*cycle*. ...##
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On the Open Packing Number of a Graph

2020
*
International journal of recent technology and engineering
*

A non-empty set of a

doi:10.35940/ijrte.d1038.1284s419
fatcat:xcwejf4j4rf25m2hyzqimwmvlm
*graph*G is an open*packing*set of G if no two vertices of S have a common neighbor*in*G. ...*In*this paper, the classes of trees and unicyclic*graphs*for which the value of is either 2 or 3 are characterized. ... Let C n be a*cycle*on 3 n vertices. Then*II*. MAIN RESULTS*In*this section we characterize the connected*graphs*for which the value of the open*packing*number is 2. ...##
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Maximum cycle packing in Eulerian graphs using local traces

2015
*
Discussiones Mathematicae Graph Theory
*

We prove that every maximum edge-disjoint

doi:10.7151/dmgt.1785
fatcat:6eo572esg5b55c4yd64tba4mxq
*cycle**packing*Z * of G induces a maximum trace T (v) at v for every v ∈ V . ... Moreover, if G is Eulerian then sufficient conditions are given that guarantee that the sets of*cycles*inducing maximum local traces of G also induce a maximum*cycle**packing*of G. ...*Packing*edge-disjoint*cycles**in**graphs*is a classical*graph*-theoretical problem. ...##
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Set packing relaxations of some integer programs

2000
*
Mathematical programming
*

(

doi:10.1007/pl00011381
fatcat:p7rw7e5i7fgill3sxzmq3fem2y
*ii*) If C is an odd*cycle**in*G, the odd*cycle*inequality i∈C x i ≤ (|C| − 1)/2 is valid for P SSP . ... Then: (i) Orthonormal representation inequalities violated by x can be separated*in*polynomial time. (*ii*) Odd*cycle*inequalities violated by x can be separated*in*polynomial time. ...*cycle*inequality*in*the link*graph*if and only if a violated*cycle*of*cycles*inequality*in*G exists ...##
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Packing (2^k+1-1)-order perfect binary trees into (k+1)-connected graph
[article]

2013
*
arXiv
*
pre-print

We also prove that the T_k

arXiv:1309.3825v1
fatcat:qb6uyasudvdblbxafhk3pw3ede
*packing*problem*in*an arbitrary*graph*is NP-hard, and propose the distributed approximation algorithms. ... Let G=(V,E) and H be two*graphs*.*Packing*problem is to find*in*G the largest number of independent subgraphs each of which is isomorphic to H. Let U⊂V. ... According to the property of 2-connected*graphs*[2] , We can reconstruct the 2-connected*graph*G*in*this way: (i) to find*in*G a*cycle*C; (*ii*)to add C-paths to C to form a*graph*H; (iii) to add H-paths ...##
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Jones' Conjecture in subcubic graphs
[article]

2019
*
arXiv
*
pre-print

We confirm Jones' Conjecture for subcubic

arXiv:1912.01570v1
fatcat:tg2tfy7pzzfqhetloigzl34grq
*graphs*. Namely, if a subcubic planar*graph*does not contain k+1 vertex-disjoint*cycles*, then it suffices to delete 2k vertices to obtain a forest. ... A*cycle**packing*of a (multi)*graph*G is a set of vertex disjoint*cycles*that appear*in*G as subgraphs. We denote the maximum size of a*cycle**packing*of G by cp(G). ... Then for i ∈ {1, 2},*in*every*cycle**packing*of G AB i there is a*cycle*containing e A and e B . ...##
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Maximum packings with odd cycles

1994
*
Discrete Mathematics
*

We show how to obtain maximum

doi:10.1016/0012-365x(94)90375-1
fatcat:3vqkhl3x55fbdc4rhcmfilts2e
*packings*of K", +v with k-*cycles*when k>3 is odd, g a positive integer, and v even with O<v< 2k. ... Moreover, under certain conditions on v, we obtain maximum*packings*of Kzkg+". ...*ii*Fi. This decomposition is a maximum*packing*of K,,,+ u since its leave is a l-factor*in*KZkg. 0 Hence, 2kg+u is k-nice. 0 Corollary 4.5. ...##
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Decomposing various graphs into short even-length cycles
[article]

2012
*
arXiv
*
pre-print

We then use this result to obtain results on incomplete even

arXiv:1204.3368v1
fatcat:gtbdsrvttnbmrfyrsadrzcsxta
*cycle*systems with a hole and on decompositions of complete multipartite*graphs*into*cycles*of uniform even length. ... We prove that a complete bipartite*graph*can be decomposed into*cycles*of arbitrary specified lengths provided that the obvious necessary conditions are satisfied, the length of each*cycle*is at most the ... Acknowledgement This research was supported*in*part by the Atlantic Association for Research*in*the Mathematical Sciences. ...
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