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Counting directed acyclic and elementary digraphs [article]

Élie de Panafieu, Sergey Dovgal
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  ... 
arXiv:2001.08659v2 fatcat:xub7jlxcvzf3vmbxajle7cgn3y

Tabulation of Noncrossing Acyclic Digraphs [article]

Marco Kuhlmann
2015 arXiv   pre-print
The same tabulation can be modified to 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] .  ... 
arXiv:1504.04993v1 fatcat:lf5durf42zchtkszzz4js3js5y

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.  ... 

Generating Functions of Some Families of Directed Uniform Hypergraphs [article]

Vonjy Rasendrahasina, Vlady Ravelomanana
2020 arXiv   pre-print
In this paper, we 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  ... 
arXiv:2005.11677v2 fatcat:i47legujtncv5n3ssaedqefbxy

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.  ... 

EVERY COUNTABLE MODEL OF SET THEORY EMBEDS INTO ITS OWN CONSTRUCTIBLE UNIVERSE

JOEL DAVID HAMKINS
2013 Journal of Mathematical Logic  
The proof uses universal 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.  ... 
doi:10.1142/s0219061313500062 fatcat:zeuxovyppfgybex6lrpjjvz2uy

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  ... 

Tight Localizations of Feedback Sets [article]

Michael Hecht, Krzysztof Gonciarz, Szabolcs Horvát
2020 arXiv   pre-print
E) 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.  ... 
arXiv:2001.01440v2 fatcat:ofc4o3fpqfe2nic7pnkd7wpdu4

A characteristic polynomial for rooted graphs and rooted digraphs

Gary Gordon, Elizabeth McMahon
2001 Discrete Mathematics  
When G is a rooted 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.  ... 
doi:10.1016/s0012-365x(00)00186-2 fatcat:yb2flencgrdrboykokj4kfenya

Propagation Rules for Graph Partitioning Constraints

Radosław Cymer
2016 Journal of Graph Algorithms and Applications  
We review existing methods 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.  ... 
doi:10.7155/jgaa.00397 fatcat:dsze7fqvwvefdleknj7ydodxmm

Classification of real Bott manifolds and acyclic digraphs

Suyoung Choi, Mikiya Masuda, Sang-il Oum
2016 Transactions of the American Mathematical Society  
Our characterization can also be described in terms of graph operations on 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.  ... 
doi:10.1090/tran/6896 fatcat:hpztdohv25gfxmgfelza2dyh4q

A directed graph generalization of chromatic quasisymmetric functions [article]

Brittney Ellzey
2017 arXiv   pre-print
In this paper, we define the chromatic quasisymmetric function of a 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.  ... 
arXiv:1709.00454v2 fatcat:rtxxvvqj45et3n62zqent24lfm

Exact enumeration of acyclic deterministic automata

Valery A. Liskovets
2006 Discrete Applied Mathematics  
Certain simple enumerative techniques developed by the author for 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)  ... 
doi:10.1016/j.dam.2005.06.009 fatcat:vvy332u2greszcc4625nih7xhi

Recognition of DFS trees: sequential and parallel algorithms with refined verifications

Ephraim Korach, Zvi Ostfeld
1993 Discrete Mathematics  
Here we present a parallel algorithm which solves this problem in O(t) time complexity 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  ... 
doi:10.1016/0012-365x(93)90375-4 fatcat:winug53ev5apznrs23fqnqe53m
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