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Packing Digraphs with Directed Closed Trails

PAUL BALISTER
2003 Combinatorics, probability & computing  
. , mt are integers with m i ≥ 3 and t i=1 m i = |E(Kn)| then Kn can be decomposed as an edge-disjoint union of closed trails of lengths m 1 , . . . , mt.  ...  We show that the compete directed graph ↔ Kn can be decomposed as an edge-disjoint union of directed closed trails of lengths m 1 , . . . , mt whenever m i ≥ 2 and m i = |E( ↔ Kn)|, except for the single  ...  Eulerian digraph G with |V (G)| ≥ N , δ + (G) = δ − (G) ≥ (1 − )|V (G)|, Packing ↔ K n with directed closed trails If G 1 and G 2 are graphs or digraphs, define a packing of G 1 into G 2 as a map f :  ... 
doi:10.1017/s0963548302005461 fatcat:cuhdzlqfbnbdxbnyqtywa4rgjq

Irregularity strength of digraphs

Mike Ferrara, Jesse Gilbert, Mike Jacobson, Thor Whalen
2009 Discrete Mathematics  
prescribed vertices in the complete symmetric digraph with loops.  ...  It is an elementary exercise to show that any non-trivial simple graph has two vertices with the same degree. This is not the case for digraphs and multigraphs.  ...  Then s(D) Fig. 1 . 1 The closed trail in K 3 and irregular labeling of C 8 associated with the deBruijn-like sequence 11233213.  ... 
doi:10.1016/j.disc.2008.05.045 fatcat:2f5l6esrdzcd5hdso3ahkvlxle

Ant Colony Optimization for the Ship Berthing Problem [chapter]

Chia Jim Tong, Hoong Chuin Lau, Andrew Lim
1999 Lecture Notes in Computer Science  
It has previously been applied to the TSP and QAP with encouraging results that demonstrate its potential.  ...  Experimental results suggest that ACO can be applied effectively to find good solutions for SBPs, with mean costs of solutions obtained in the experiment on difficult (compact) cases ranging from 0% to  ...  (or come too close) with over blocks which have been packed, or any other constraint to be violated.  ... 
doi:10.1007/3-540-46674-6_30 fatcat:ni62uarkjnctjfkkheelmduuze

On r-Simple k-Path and Related Problems Parameterized by k/r [article]

Gregory Gutin, Magnus Wahlström, Meirav Zehavi
2020 arXiv   pre-print
For p-Set (r,q)-Packing, we obtain a polynomial kernel for any fixed p, which resolves a question posed by Gabizon et al. regarding the existence of polynomial kernels for problems with relaxed disjointness  ...  In the r-Simple k-Path problem, given a digraph G on n vertices and integers r,k, decide whether G has an r-simple k-path, which is a walk where every vertex occurs at most r times and the total number  ...  A directed acyclic graph (DAG) is a digraph with no directed cycle.  ... 
arXiv:1806.09108v2 fatcat:hcu4slsv7rbcra5yt53qunx32a

Weights which respect support and NN-decoding [article]

Roberto Assis Machado, Marcelo Firer
2019 arXiv   pre-print
We show how these metrics can be obtained from the edge-weighted Hamming cube and, based on this representation we give a description of a group of linear isometries (with respect to the metric).  ...  The previous proposition implies that the set of all S-weights endowed with directed sum or k-sum is a magma, i.e., the set of all weights is closed under "⊕ k ".  ...  We say that δ is in a standard form if, given a trail τ with δ(τ ) = k > 1 there is a trail τ such that δ(τ ) = k − 1.  ... 
arXiv:1804.07809v2 fatcat:nrge5rqh2vcfdirfac7safaeu4

Paintshop, odd cycles and necklace splitting

Frédéric Meunier, András Sebő
2009 Discrete Applied Mathematics  
More generally, the "paint shop scheduling problem" is defined with an arbitrary multiset of colors given for each car, where this multiset has the same size as the number of occurrences of the car; the  ...  A resulting two-way reduction to a special minimum uncut problem leads to polynomial algorithms for subproblems, to observing APX-hardness through MAX CUT in 3-regular graphs, and to a solution with at  ...  It is 0 if and only if the trail is closed, in which case G is called Eulerian. We will call connected graphs with two odd degree vertices almost Eulerian.  ... 
doi:10.1016/j.dam.2008.06.017 fatcat:duawvsavaveolplqblud3y7wdq

Master index of volumes 151–160

1997 Discrete Mathematics  
Lai, Graphs without spanning closed trails Catlin, P.A., The reduction of graph families closed under contraction Caulfield, M.J., Full and quarter plane complete infinite latin squares (Note) Ceccherini  ...  Pule, An alternative formula for the number of Euler trails for a class of digraphs (Note) Marshall, S., On the existence of k-tournaments with given automorphism group Martini, H., Shadow-boundaries of  ... 
doi:10.1016/s0012-365x(97)90002-9 fatcat:jhdpq4lxr5cz5ctggxfuouj6ti

A method for optimizing waste collection using mathematical programming: a Buenos Aires case study

Flavio Bonomo, Guillermo Durán, Frederico Larumbe, Javier Marenco
2011 Waste Management & Research  
The application of the proposed method minimized the distance travelled by each collection vehicle in the areas studied, with actual reductions ranging from 10% to 40% of the existing routes.  ...  Figure 5 . 5 Model digraph G 2 with a non-directed graph G 3 . Example of the transformation defined in Section 3.4.  ...  The TSP consists in finding the shortest Hamiltonian circuit (a trail that visits each node of a graph or digraph exactly once and returns to the starting node).  ... 
doi:10.1177/0734242x11402870 pmid:21460074 fatcat:74wppiale5a2rfp7banyl5qt64

Graph Theory [article]

Jesse D. Gilbert
2015 arXiv   pre-print
Packings Consider the problem of packing P 5 or C 4 in subgraphs of K 32 . It is easy to verify that fairly dense graphs in K 32 admit dense packings of either of the two graphs.  ...  Out-direct the tree from an arbitrary leaf.  ... 
arXiv:1102.1087v9 fatcat:t5xcpwtd4bablnmyxpolq7cqim

Subject Index Volumes 1–200

2001 Discrete Mathematics  
, 5019 digraph, 3242, 5166, 5900 directed graph, 4415 multipartite digraph, 4888, 4992, 5019, 5096, 5112, 5990, see also SMD n-partite digraph, 5990 semidecomposability of a graph, 2180 semidefinite  ...  , 1848, 1996, 3248, 3405, 3797, 4490, 4674, 4836, 5019, 5096, 5112, 5246, 5371, 5915, 6013 directed graph, 939, 1146 acyclic disconnection, 5965 of a digraph, 5965 acyclic dominating set, 5053 forbidden  ...  , 1350, 1604, 1985 r-digraph, see n-digraph r-dimensional, see n-dimensional r-dominating, see n-dominating r-domination, see n-domination r-extension, see n-extension r-graph, 1, see n-graph r-initial  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Discrete relaxations of combinatorial programs

Ralf Borndörfer, Robert Weismantel
2001 Discrete Applied Mathematics  
We show that knapsack and set packing relaxations give rise to combinatorial cutting planes in a simple and straightforward way. The constructions are algorithmic. ?  ...  The Steiner tree problem The Steiner tree problem in directed graphs involves a digraph D = (V; A) with weights w a ∈ Q + on its arcs and a node set T ⊆ V of terminals, one of them, say r ∈ T , is the  ...  The cycle inequalities of this relaxation are known as the odd closed alternating trail inequalities. The separation problem has been solved by Caprara and Fischetti [4] .  ... 
doi:10.1016/s0166-218x(00)00307-3 fatcat:vg3bc6nadfdynmxn5zhous477u

Master index of volumes 181–190

1998 Discrete Mathematics  
Lindner, The Doyen-Wilson theorem for maximum packings of Kn with 4-cycles Fu, H.-L., see B.-L.  ...  ., Directed covering with block size 5 and index even 188 (1998) Bae, J., An extremal problem for subset-sum-distinct sequences with congruence conditions 189 (1998) Bagchi, B. and B.  ... 
doi:10.1016/s0012-365x(98)90328-4 fatcat:s2tsivncvfcilf6jlbl4fx24zq

Optimized Assembly Design for Resource Efficient Production in a Multiproduct Manufacturing System

Oliver Gould, Alessandro Simeone, James Colwill, Elliot Woolley, Roy Willey, Shahin Rahimifard
2017 Procedia CIRP  
Let be a given complete digraph, be the vertex set, and be a cost associated with the arc .  ...  (with The TSP is the problem of finding a minimal cost closed tour (Hamiltonian circuit) of V that visits each vertex of A exactly once [12] .  ... 
doi:10.1016/j.procir.2016.06.114 fatcat:xslqqxbsnvew3c6hixczlbgiae

Book announcements

1990 Discrete Applied Mathematics  
Identifying relative voltages with permu- tation voltages). Subgroups of the voltage group (The fundamental semigroup of closed walks. Counting components of ordinary derived graphs.  ...  Trouble with constraints. The basic algorithm. Optimi- zation problems with inexact data. Convergence properties. Accelerating devices: Overview.  ... 
doi:10.1016/0166-218x(90)90074-m fatcat:uhwd4fl3wvcetkvers2zklsbry

Master index of volumes 111–120

1993 Discrete Mathematics  
-H., Spanning closed trails in graphs Chen, Z., see Chao, C.-Y. Chilakamarri, K.B. and P. Hamburger, On a class of kernel- perfect and kernel-perfect-critical graphs (Note) Chiricota, Y. and G.  ...  Double commutative- step digraphs with minimum diameters 111 (1993) 165-178 118 (1993) 45-56 114 (1993) 1155129 113 (1993) 2599262 113 (1993) 59-70 111 (1993) 189-196 111 (1993) 179-188  ...  Tuza, Menger-type theorems with restric-112 (1993) 165-172 115 (1993) 51-55 118 (1993) 295-297 114 (1993) 379-401 111 (1993) 423-434 111 (1993) 145-156 115 (1993) 231-244 118 (1993) 33  ... 
doi:10.1016/0012-365x(93)90129-h fatcat:hwvjojuebjfdpmlzhvc3ndowem
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