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Packing Digraphs with Directed Closed Trails

2003
*
Combinatorics, probability & computing
*

. , mt are integers

doi:10.1017/s0963548302005461
fatcat:cuhdzlqfbnbdxbnyqtywa4rgjq
*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 : ...##
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Irregularity strength of digraphs

2009
*
Discrete Mathematics
*

prescribed vertices in the complete symmetric

doi:10.1016/j.disc.2008.05.045
fatcat:2f5l6esrdzcd5hdso3ahkvlxle
*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. ...##
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Ant Colony Optimization for the Ship Berthing Problem
[chapter]

1999
*
Lecture Notes in Computer Science
*

It has previously been applied to the TSP and QAP

doi:10.1007/3-540-46674-6_30
fatcat:ni62uarkjnctjfkkheelmduuze
*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. ...##
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On r-Simple k-Path and Related Problems Parameterized by k/r
[article]

2020
*
arXiv
*
pre-print

For p-Set (r,q)-

arXiv:1806.09108v2
fatcat:hcu4slsv7rbcra5yt53qunx32a
*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. ...##
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Weights which respect support and NN-decoding
[article]

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 (

arXiv:1804.07809v2
fatcat:nrge5rqh2vcfdirfac7safaeu4
*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. ...##
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Paintshop, odd cycles and necklace splitting

2009
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Discrete Applied Mathematics
*

More generally, the "paint shop scheduling problem" is defined

doi:10.1016/j.dam.2008.06.017
fatcat:duawvsavaveolplqblud3y7wdq
*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. ...##
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Master index of volumes 151–160

1997
*
Discrete Mathematics
*

Lai, Graphs without spanning

doi:10.1016/s0012-365x(97)90002-9
fatcat:jhdpq4lxr5cz5ctggxfuouj6ti
*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 ...##
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A method for optimizing waste collection using mathematical programming: a Buenos Aires case study

2011
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Waste Management & Research
*

The application of the proposed method minimized the distance travelled by each collection vehicle in the areas studied,

doi:10.1177/0734242x11402870
pmid:21460074
fatcat:74wppiale5a2rfp7banyl5qt64
*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). ...##
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Graph Theory
[article]

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. ...

##
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Subject Index Volumes 1–200

2001
*
Discrete Mathematics
*

, 5019

doi:10.1016/s0012-365x(00)00471-4
fatcat:znxg54q6ifgutnhzj3urcw455y
*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 ...##
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Discrete relaxations of combinatorial programs

2001
*
Discrete Applied Mathematics
*

We show that knapsack and set

doi:10.1016/s0166-218x(00)00307-3
fatcat:vg3bc6nadfdynmxn5zhous477u
*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] . ...##
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Master index of volumes 181–190

1998
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Discrete Mathematics
*

Lindner, The Doyen-Wilson theorem for maximum

doi:10.1016/s0012-365x(98)90328-4
fatcat:s2tsivncvfcilf6jlbl4fx24zq
*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. ...##
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Optimized Assembly Design for Resource Efficient Production in a Multiproduct Manufacturing System

2017
*
Procedia CIRP
*

Let be a given complete

doi:10.1016/j.procir.2016.06.114
fatcat:xslqqxbsnvew3c6hixczlbgiae
*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] . ...##
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Book announcements

1990
*
Discrete Applied Mathematics
*

Identifying
relative voltages

doi:10.1016/0166-218x(90)90074-m
fatcat:uhwd4fl3wvcetkvers2zklsbry
*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. ...##
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Master index of volumes 111–120

1993
*
Discrete Mathematics
*

-H., Spanning

doi:10.1016/0012-365x(93)90129-h
fatcat:hwvjojuebjfdpmlzhvc3ndowem
*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 ...
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