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Independent Domination in Directed Graphs
[article]

2019
*
arXiv
*
pre-print

We show that

arXiv:1909.05121v1
fatcat:tlctu3nwjja6vpa2xsnnp4q3ku
*an*independent*dominating**set**of**an**orientation**of**a*graph is also*an*independent*dominating**set**of**the*underlying graph, but that*the*converse is not true in general. ... We also provide*the*idomatic*number*for special cases*of*some*of*these families*of*digraphs. ...*Trees*We next turn our attention to*orientations**of**trees*by proving*an*existence theorem for all*orientations**of**trees*. Theorem 4. Every*oriented**tree**admits**an*independent*dominating**set*, Proof. ...##
###
Page 7332 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
*
Mathematical Reviews
*

We also examine

*the*maximum*number*y,*of**orientations**admitting**an**efficient**dominating**set*in*a**tree*with g edges. ... , Anthony E. (1-WILC; La Crosse, W1); Clark, Lane H. (1-SIL; Carbondale, IL)*The**number**of**orientations**of**a**tree**admitting**an**efficient**dominating**set*. ...##
###
Page 2313 of Mathematical Reviews Vol. , Issue 86f
[page]

1986
*
Mathematical Reviews
*

*The*

*set*D is

*a*total

*dominating*

*set*in G if every vertex

*of*G is adjacent to some vertex

*of*D, and D is

*an*independent

*dominating*

*set*in G if D is

*a*

*dominating*

*set*and D is also independent. ...

*The*minimum orders

*of*

*dominating*

*sets*, total

*dominating*

*sets*, and independent

*dominating*

*sets*, denoted 7(G), +:(G) and 7(G), respectively, are called

*the*

*domination*

*number*,

*the*total

*domination*

*number*...

##
###
Efficient total domination in digraphs

2012
*
Journal of Discrete Algorithms
*

*An*

*efficiently*total

*dominating*

*set*X

*of*

*a*digraph D is

*a*vertex subset such that every vertex

*of*D has exactly one predecessor in X. ... We study graphs that permit

*an*

*orientation*having such

*a*

*set*and give complexity results and characterizations. ... Acknowledgement I am indebted to

*an*anonymous referee, whose careful suggestions helped to improve

*the*presentation

*of*

*the*paper

*a*lot. ...

*The*problem has been studied, among others, in

*the*context

*of*causal discovery, and it is known that it reduces to counting

*the*

*number*

*of*so-called moral acyclic

*orientations*

*of*certain undirected graphs ... We consider

*the*problem

*of*counting

*the*

*number*

*of*DAGs which are Markov-equivalent, i.e., which encode

*the*same conditional independencies between random variables. ... Robert Ganian and Thekla Hamm acknowledge support from

*the*Austrian Science Fund (FWF, Project P31336: NFPC). Thekla Hamm is co-funded by FWF project W1255-N23. ...

##
###
Forthcoming Papers

1990
*
Discrete Mathematics
*

(such as being

doi:10.1016/0012-365x(90)90253-e
fatcat:lsnnd2ldijfchkvoahxk76tfdy
*a*minimum*dominating**set*) or finding*a*partition*of**the*vertex*set*into such*sets*(for example,*a*partition into*the*maximum possible*number**of**dominating**sets*). ... We study*a*new version*of**the**domination*problem in which*the**dominating**set*is required to be*a*clique. ...*The*least*domination**number*y,(G)*of*G is*the*minimum cardinality*of**an*1.d.s. If v, is*the*total*domination**number*, we prove among other things: 0) v1 s v,, (ii) for*a**tree*, vr s or. ...##
###
Plane Geometric Graph Augmentation: A Generic Perspective
[chapter]

2012
*
Thirty Essays on Geometric Graph Theory
*

*The*geometric constraints on

*the*possible new edges render some

*of*

*the*simplest augmentation problems intractable, and in many cases only extremal results are known. ... We consider augmentation problems over plane geometric graphs, that is, graphs given with

*a*crossing-free straight-line embedding in

*the*plane. ... They also show that every multigraph that has

*an*even

*number*

*of*edges and contains two edge-disjoint spanning

*trees*must have

*a*conflict-free even

*orientation*. ...

##
###
Page 4741 of Mathematical Reviews Vol. , Issue 911
[page]

1991
*
Mathematical Reviews
*

Summary: “

*A*graph G has*tree*-width at most w if it*admits**a**tree*-decomposition*of*width < w. ... Summary: “*Efficient*algorithms are developed for finding*a*min- imum cardinality connected*dominating**set*and*a*minimum car- dinality Steiner*tree*in permutation graphs. ...##
###
Counting and Sampling Markov Equivalent Directed Acyclic Graphs

2019
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

These problems

doi:10.1609/aaai.v33i01.33017984
fatcat:k2shllueuzbspa422l2vxl767q
*efficiently*reduce to counting*the*moral acyclic*orientations**of**a*given undirected connected chordal graph on n vertices, for which we give two algorithms. ... 2kk2n) operations, where k is*the*size*of**the*largest clique in*the*graph; for bounded-degree graphs this bound is linear in n. ... Acknowledgments This work was supported in part by*the*Academy*of*Finland, under Grant 276864. ...##
###
Fast algorithms for finding Hamiltonian paths and cycles in in-tournament digraphs

1993
*
Discrete Applied Mathematics
*

*An*in-tournament digraph is

*a*digraph in which

*the*

*set*

*of*in-neighbours

*of*every vertex induces

*a*tournament. ... Here n, m denote

*the*

*number*

*of*vertices respectively arcs

*of*

*the*in-tournament digraph. ...

*A*local tournament digraph (local tournament for short) [2, 51 , is

*an*

*oriented*graph in which

*the*

*set*

*of*in-neighbours as well as

*the*

*set*

*of*out-neighbours

*of*each vertex induce

*a*tournament. ...

##
###
Locating-dominating sets: from graphs to oriented graphs
[article]

2022
*
arXiv
*
pre-print

*A*locating-

*dominating*

*set*in

*an*

*oriented*graph is

*a*

*set*S such that for every w∈ V, N[w]^-∩ S=∅ and for each pair

*of*vertices u,v∈ V∖ S, N^-(u)∩ S N^-(v)∩ S. We consider

*the*following two parameters. ... Given

*an*undirected graph G, we look for →γ_LD(G) (→Γ_LD(G)) which is

*the*size

*of*

*the*smallest (largest) optimal locating-

*dominating*

*set*over all

*orientations*

*of*G. ... Moreover, if we take

*a*cyclic

*orientation*

*of*C n ,

*the*

*set*

*of*vertices with

*an*odd index

*number*forms

*an*optimal locating-

*dominating*

*set*. ...

##
###
Algorithmic Properties of Sparse Digraphs
[article]

2017
*
arXiv
*
pre-print

More specifically, we show that

arXiv:1707.01701v2
fatcat:u5dw74mn6rgbjbtimlczufecbu
*the*directed Steiner*tree*problem is fixed-parameter tractable on any class*of*directed bounded expansion parameterized by*the**number*k*of*non-terminals plus*the*maximal ... up to*a*factor O(k· k) on any class*of*directed bounded expansion, where k denotes*the*size*of**an*optimal solution. ... Most generally, it*admits**an*O(log k) approximation on graphs*of*bounded VC-dimension [9] (where k is*the*size*of**an*optimal*dominating**set*). ...##
###
Recognition and Orientation Algorithms for P4-Comparability Graphs
[chapter]

2001
*
Lecture Notes in Computer Science
*

P4-transitive

doi:10.1007/3-540-45678-3_28
fatcat:aksvlgko2jbdzdv4oqeoh7etve
*orientation**of**a*P4-comparability graph. ... We consider two problems pertaining to P4-comparability graphs, namely,*the*problem*of*recognizing whether*a*simple undirected graph is*a*P4-comparability graph and*the*problem*of*producing*an*acyclic ...*A*graph which*admits**an*acyclic transitive*orientation*is called*a*comparability graph [3, 4] ;*A*graph is*a*P 4 -comparability graph if it*admits**an*acyclic P 4 -transitive*orientation*[5, 6] . ...##
###
Survey of local algorithms

2013
*
ACM Computing Surveys
*

*A*local algorithm is

*a*distributed algorithm that runs in constant time, independently

*of*

*the*size

*of*

*the*network. ... Encoding

*of*input and output. When we study local algorithms, we assume that

*the*problem instance is given in

*a*distributed manner: each node in

*the*communication graph G knows part

*of*

*the*input. ...

*A*preliminary version

*of*this survey was published as

*a*part

*of*my PhD thesis [134, §2]. Updates to this work will be posted online at http://www. ...

##
###
Splitting trees

1997
*
Discrete Mathematics
*

*An*O(N) algorithm is proposed to get

*an*upper bound c'(t),

*the*connected splitting

*number*, on

*the*splitting

*number*o(t)

*of*

*a*

*tree*T and

*an*O(N log N) algorithm to compute this last

*number*, where N is

*the*...

*number*

*of*vertices

*of*

*the*

*tree*. ... Acknowledgements Work

*of*

*the*first author was done during

*a*visit to ficole Polytechnique Ftdtrale de Lausanne, whose hospitality is gratefully acknowledged. ...

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