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Packing Strong Subgraph in Digraphs [article]

Yuefang Sun, Gregory Gutin, Xiaoyan Zhang
2021 arXiv   pre-print
In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem.  ...  We first prove the NP-completeness for the internally disjoint strong subgraph packing problem restricted to symmetric digraphs and Eulerian digraphs.  ...  The Steiner tree packing problem has applications in a number of areas such as VLSI circuit design [14, 25] and stream broadcasting [21] .  ... 
arXiv:2110.12783v1 fatcat:kikggvpihrfznkrk2bzfkuambu

Steiner Type Packing Problems in Digraphs: A Survey [article]

Yuefang Sun
2022 arXiv   pre-print
In this survey we overview known results on several Steiner type packing problems in digraphs.  ...  The paper is divided into five sections: introduction, directed Steiner tree packings, strong subgraph packings, strong arc decomposition, arc-disjoint cycles containing given vertices.  ...  The Steiner tree packing problem has applications in VLSI circuit design [17, 33] . In this application, a Steiner tree is needed to share an electronic signal by a set of terminal nodes.  ... 
arXiv:2206.12092v1 fatcat:rqexgiz2nzew5amvdra6x6aivm

Page 6599 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
tours in iterated line digraphs.  ...  (F-PARIS6-CM; Paris); Robertson, Neil (1-OHS; Columbus, OH); Seymour, Paul (1-BELL6; Morristown, NJ); Thomas, Robin (1-GAIT; Atlanta, GA) Packing directed circuits.  ... 

Optimal Index Codes With Near-Extreme Rates

Son Hoang Dau, Vitaly Skachek, Yeow Meng Chee
2014 IEEE Transactions on Information Theory  
In addition, a circuit-packing bound is revisited, and several families of digraphs, optimal with respect to this bound, whose min-ranks can be found in polynomial time, are presented.  ...  In this paper, the graphs and digraphs of near-extreme min-ranks are studied.  ...  CIRCUIT-PACKING BOUND REVISITED In this section, we discuss a circuit-packing bound [23] for the min-rank of a digraph.  ... 
doi:10.1109/tit.2013.2295331 fatcat:ylcnjvefdjhqjeygevszryu3ge

Optimal index codes with near-extreme rates

Son Hoang Dau, Vitaly Skachek, Yeow Meng Chee
2012 2012 IEEE International Symposium on Information Theory Proceedings  
In addition, a circuit-packing bound is revisited, and several families of digraphs, optimal with respect to this bound, whose min-ranks can be found in polynomial time, are presented.  ...  In this paper, the graphs and digraphs of near-extreme min-ranks are studied.  ...  CIRCUIT-PACKING BOUND REVISITED In this section, we discuss a circuit-packing bound [23] for the min-rank of a digraph.  ... 
doi:10.1109/isit.2012.6283852 dblp:conf/isit/DauSC12 fatcat:viohjeqm6bhqfbthzflea5pjl4

Parameterized Tractability of Edge-Disjoint Paths on Directed Acyclic Graphs [chapter]

Aleksandrs Slivkins
2003 Lecture Notes in Computer Science  
We consider this problem on acyclic digraphs. It is known to be NP-complete and solvable in time n O(k) where n is the number of nodes.  ...  n) algorithm for the special case when G is acyclic and G + H is Eulerian, where H is the demand graph.  ...  We focus on Eulerian digraphs, a natural and well-known class of digraphs. (A digraph is called Eulerian if for each vertex the in-degree is equal to the out-degree.)  ... 
doi:10.1007/978-3-540-39658-1_44 fatcat:ziapmseqyngvtbvylnvezo2cqm

Free multiflows in bidirected and skew-symmetric graphs

Maxim A. Babenko, Alexander V. Karzanov
2007 Discrete Applied Mathematics  
In particular, this improves the best known bound for digraphs.  ...  A similar relation for inner Eulerian digraphs was established by Lomonosov.  ...  Acknowledgments We thank the anonymous referees for suggesting improvements in the original version of this paper.  ... 
doi:10.1016/j.dam.2007.02.012 fatcat:q54lzmrwjra2rfuncrulffkgvm

Page 4071 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
D. (1-BELL6; Morristown, NJ) Packing circuits in Eulerian digraphs. (English summary) Combinatorica 16 (1996), no. 2, 223-231.  ...  Let G be an Eulerian digraph; let v(G) be the maximum number of pairwise edge-disjoint directed circuits of G, and t(G) the smallest size of a set of edges that meets all directed circuits of G.  ... 

Free multiflows in bidirected and skew-symmetric graphs [article]

M.A. Babenko, A.V. Karzanov
2005 arXiv   pre-print
In particular, this improves the known bound for digraphs.  ...  A similar relation for inner Eulerian digraphs was established by Lomonosov.  ...  Given an IS-multiflow F in (G, T, c), represent each flow f st in the path packing form: (13) f st = α 1 χ P 1 + . . . + α k χ P k , where α i = α(P i ) ∈ Z + and P i is a circuit or a (simple) path  ... 
arXiv:math/0510463v1 fatcat:qotxvxaycfcrpb4d27flzx6wv4

An Improved Algorithm for Packing T-Paths in Inner Eulerian Networks [chapter]

Maxim A. Babenko, Kamil Salikhov, Stepan Artamonov
2012 Lecture Notes in Computer Science  
A digraph G = (V, E) with a distinguished set T ⊆ V of terminals is called inner Eulerian if for each v ∈ V − T the numbers of arcs entering and leaving v are equal.  ...  Preliminaries Introduction Computing a maximum integer flow, i.e. a maximum packing of paths connecting a given pair of terminals subject to edge capacities, is widely regarded as a central problem in  ...  A maximum integer multiflow in an inner Eulerian digraph G = (V, E) with terminals T ⊆ V can be found in O(φ(V, E) · log T + E log V ) time.  ... 
doi:10.1007/978-3-642-32241-9_10 fatcat:p4ns4uu2nbdj3gv63h2u2alt74

Research Problems from the Fourth Cracow Conference (Czorsztyn, 2002)

Rafał Kalinowski, Mariusz Meszka
2007 Discrete Mathematics  
One may also ask such 'nomadic' questions about Euler tours in eulerian graphs.  ...  Does the complete n-vertex digraph admit a nomadic (n − 1)-circuit decomposition, for sufficiently large n?  ...  It was conjectured in [1] that when n is sufficiently large in terms of k, every simple n-vertex graph G with more than 3 2 k − 2 (n − k + 1) edges has a k-connected subgraph (for k 7, it may suffice  ... 
doi:10.1016/j.disc.2006.09.039 fatcat:r2z7zf5vmjdu5pb2gmbgpo33wi

A survey on flows in graphs and matroids

Bertrand Guenin
2016 Discrete Applied Mathematics  
We will not assume from the reader any background in matroid theory.  ...  We survey generalizations of these results to multi-commodity flows and to flows in binary matroids.  ...  In particular, P 10 is Eulerian. Thus we have seen four examples of Eulerian signed matroids that do not pack.  ... 
doi:10.1016/j.dam.2015.10.035 fatcat:7tg2bn5czvclzeegpjzf4e3nmi

Introduction to graph theory

1981 Discrete Mathematics  
Paths and circuits. 5. Moue defini- c tions. 6. Eulerian graphs. 7. Hamiltonian graphs. 8. Some applications. Chapter 4. Trees. Q. chromatic number. 18. Two proofs. 19.  ...  Construction of an example in each admissible re .i'* Be class. 3. Some recursive constructions. References. 6. Packing and coverin? of (:)-sets l-w + E. Brouwer. Introduction. I.  ... 
doi:10.1016/0012-365x(81)90150-3 fatcat:drh6oy32fbehfc7e7rcopeayqu

Page 3801 of Mathematical Reviews Vol. , Issue 85i [page]

1985 Mathematical Reviews  
The authors give a new method for generating all Eulerian circuits in an Eulerian digraph. Fan R. K. Chung (Murray Hill, N.J.) Gardiner, A. (4-BIRM); McAvaney, K.  ...  Zhang, Fu Ji; Lin, Guo Ning (PRC-LAN) 85i:05123 A graphical method for generating all Euler tours of an Eulerian digraph. (Chinese. English summary) Lanzhou Darue Xuebao 19 (1983), no. 2, 1-9.  ... 

On circuit decomposition of planar Eulerian graphs

Herbert Fleischner, András Frank
1990 Journal of combinatorial theory. Series B (Print)  
In order to have hope to get an integer packing of circuits it is obviously necessary for f that 2(f(e) : e incident to v) is even for every v E I/. Such an f is called Eulerian.  ...  ., [2] ) can be interpreted as one giving a necessary and sufficient condition for the existence of a list of directed circuits of a digraph so that the number of circuits from the list containing any  ... 
doi:10.1016/0095-8956(90)90080-j fatcat:xvdoawsbbrhc7lhnj5yldmkf6m
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