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Counting directed acyclic and elementary digraphs
[article]

2020
*
arXiv
*
pre-print

*digraph*is

*acyclic*is an explicit function p(c), such that p(0) = 1

*and*p(1) = 0. ... We call such

*digraphs*

*elementary*

*digraphs*. We express the probability that a random

*digraph*is

*elementary*as a function of μ. ... We are grateful to Olivier Bodini, Naina Ralaivaosaona, Vonjy Rasendrahasina, Vlady Ravelomanana,

*and*Stephan Wagner for fruitful discussions,

*and*to the anonyomous referees whose suggestions helped to ...

##
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Tabulation of Noncrossing Acyclic Digraphs
[article]

2015
*
arXiv
*
pre-print

The same tabulation can be modified to

arXiv:1504.04993v1
fatcat:lf5durf42zchtkszzz4js3js5y
*count*other classes of combinatorial structures, including weakly connected noncrossing*acyclic**digraphs*, general noncrossing*digraphs*, noncrossing undirected graphs ... As an illustration, along with this note I am releasing the implementation of an algorithm for*counting*the number of noncrossing*acyclic**digraphs*of a given size. ... Acknowledgments The decomposition that is the basis for the tabulation presented in this note was inspired by a*counting*technique for noncrossing*acyclic**digraphs*proposed by Tirrell [2014] . ...##
###
Page 1396 of Mathematical Reviews Vol. , Issue 98C
[page]

1998
*
Mathematical Reviews
*

Let S,H,

*and*T denote three disjoint subsets of vertices of an*acyclic**directed*graph G with non-negative edge weights. ... |Lee, Der Tsai] (1-NW-E; Evanston, IL) Steiner problems on*directed**acyclic*graphs. (English summary) Computing*and*combinatorics (Hong Kong, 1996), 21-30, Lecture Notes in Comput. ...##
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Generating Functions of Some Families of Directed Uniform Hypergraphs
[article]

2020
*
arXiv
*
pre-print

In this paper, we

arXiv:2005.11677v2
fatcat:i47legujtncv5n3ssaedqefbxy
*count**acyclic**and*strongly connected uniform*directed*labeled hypergraphs. ... For these combinatorial structures, we introduce a specific generating function allowing us to recover*and*generalize some results on the number of*directed**acyclic*graphs*and*the number of strongly connected ... We notice also that a different approach has been given by Ostroff [23] to*count*strong*digraphs*Let us recall that Robinson [27, Corollary 1] showed that the*counting*sequence α n (y) of*acyclic**digraphs*...##
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Page 4772 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

98h:05083
application to the

*counting*of |-factors of de Bruijn*and*Kautz*digraphs*.” ... In this paper we discuss the multiplicativity of*acyclic*Hamiltonian*digraphs*, i.e.,*acyclic**digraphs*which contain a Hamiltonian path. ...##
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EVERY COUNTABLE MODEL OF SET THEORY EMBEDS INTO ITS OWN CONSTRUCTIBLE UNIVERSE

2013
*
Journal of Mathematical Logic
*

The proof uses universal

doi:10.1142/s0219061313500062
fatcat:zeuxovyppfgybex6lrpjjvz2uy
*digraph*combinatorics, including an*acyclic*version of the countable random*digraph*, which I call the countable random Q-graded*digraph*,*and*higher analogues arising as uncountable ... The proof shows that L^M contains a submodel that is a universal*acyclic**digraph*of rank Ord^M. ... A*digraph*is*acyclic*if there is no finite*directed*path from a vertex to itself. That is, an*acyclic**digraph*is one with no*directed*cycles. ...##
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Page 2124 of Mathematical Reviews Vol. , Issue 97D
[page]

1997
*
Mathematical Reviews
*

Specializations of the Tutte polynomial

*count*various objects associated with G, e.g., subgraphs, spanning trees,*acyclic*orientations, inversions*and*parking functions. ... The conventional approach uses determinants,*and*explicit formulas have been found for several families of graphs, undirected*and**directed*. ...##
###
Page 3022 of Mathematical Reviews Vol. , Issue 84h
[page]

1984
*
Mathematical Reviews
*

As an application,

*acyclic*orientations of signed graphs are*counted*. In the third paper, the forest lattice*and*bicircular matroids are studied in their context. ... Author’s introduction: “Gallai*and*Milgram have shown that in a*directed*graph, the minimum number of vertex-disjoint (*elementary*,*directed*) paths needed to cover the vertex-set is smaller than or equal ...##
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Tight Localizations of Feedback Sets
[article]

2020
*
arXiv
*
pre-print

E)

arXiv:2001.01440v2
fatcat:ofc4o3fpqfe2nic7pnkd7wpdu4
*acyclic*, respectively. ... The classical NP-hard feedback arc set problem (FASP)*and*feedback vertex set problem (FVSP) ask for a minimum set of arcs ε⊆ E or vertices ν⊆ V whose removal G∖ε, G∖ν makes a given multi-*digraph*G=(V, ... The cycle c 0 = {e, f , д, h, k, l, m, o, n} is a simple*and*non-*elementary*cycle, while the cycles c 1 = {e, f , д, h, k, n}*and*c 2 = {o, l, m} are*elementary*. ...##
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A characteristic polynomial for rooted graphs and rooted digraphs

2001
*
Discrete Mathematics
*

When G is a rooted

doi:10.1016/s0012-365x(00)00186-2
fatcat:yb2flencgrdrboykokj4kfenya
*digraph*, we show that this polynomial essentially*counts*the number of sinks in G. ... In particular, |p(G; 0)| is the number of*acyclic*orientations of G, while the degree of p(G; ) gives the size of the minimum tree cover (every edge of G is adjacent to some edge of T ),*and*the leading ... Proof: First, note that if a*digraph*D has no*directed*cycles, then it must have at least one sink. Assume that D is a rooted*digraph*with no greedoid loops*and*no*directed*cycles. ...##
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Propagation Rules for Graph Partitioning Constraints

2016
*
Journal of Graph Algorithms and Applications
*

We review existing methods

doi:10.7155/jgaa.00397
fatcat:dsze7fqvwvefdleknj7ydodxmm
*and*present a generic propagation mechanism for graph partitioning constraints based on*directed*matchings. ... Every solution of the global constraint corresponds to a subgraph of the corresponding*digraph*associated with the constraint. ... Acknowledgements The author wish to thank anonymous referees for their valuable comments*and*suggestions that have considerably improved the presentation of this paper. ...##
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Classification of real Bott manifolds and acyclic digraphs

2016
*
Transactions of the American Mathematical Society
*

Our characterization can also be described in terms of graph operations on

doi:10.1090/tran/6896
fatcat:hpztdohv25gfxmgfelza2dyh4q
*directed**acyclic*graphs. ... Finally, we produce some numerical invariants of real Bott manifolds from the viewpoint of graph theory*and*discuss their topological meaning. ... To a matrix A of B(n), one can associate an*acyclic**digraph*(a*directed*graph with no*directed*cycles) whose adjacency matrix is A. ...##
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A directed graph generalization of chromatic quasisymmetric functions
[article]

2017
*
arXiv
*
pre-print

In this paper, we define the chromatic quasisymmetric function of a

arXiv:1709.00454v2
fatcat:rtxxvvqj45et3n62zqent24lfm
*directed*graph, which agrees with the Shareshian-Wachs definition in the*acyclic*case. ... Stanley defined the chromatic symmetric function of a graph,*and*Shareshian*and*Wachs introduced a refinement, namely the chromatic quasisymmetric function of a labeled graph. ... I would also like to thank my advisor, Michelle Wachs, for all of her guidance*and*encouragement. ...##
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Exact enumeration of acyclic deterministic automata

2006
*
Discrete Applied Mathematics
*

Certain simple enumerative techniques developed by the author for

doi:10.1016/j.dam.2005.06.009
fatcat:vvy332u2greszcc4625nih7xhi
*counting*initially connected automata*and**acyclic**digraphs*are combined*and*applied. ... The latter determines, in particular, the number of*acyclic*automata with labelled states. ... There are also formulae in terms of Stirling numbers*and*Dyck paths,*and*some similar formulae for C (1) ...##
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Recognition of DFS trees: sequential and parallel algorithms with refined verifications

1993
*
Discrete Mathematics
*

Here we present a parallel algorithm which solves this problem in O(t) time complexity

doi:10.1016/0012-365x(93)90375-4
fatcat:winug53ev5apznrs23fqnqe53m
*and*uses 0( jEl/t) processors, where t>log 1 VI, on a CREW PRAM. We also study the problem for*directed*graphs. ... In the*directed*case, if T is not a DFS tree in G then the sequential algorithm supplies an 0 (I VI) time proof for that fact*and*the parallel implementation supplies a proof for the fact that can be verified ... Acknowledgments We thank Baruch Schieber for providing Lemma 3.7*and*for improving the implementation complexity of algorithm PAR CHECK that we got in a previous manu-_ script, as stated in Theorem 3.8 ...
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