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The connectivity of acyclic orientation graphs

1998
*
Discrete Mathematics
*

*The*

*acyclic*

*orientation*

*graph*, AO(G),

*of*an undirected

*graph*, G, is

*the*

*graph*whose vertices are

*the*

*acyclic*

*orientations*

*of*G and whose edges are

*the*pairs

*of*

*orientations*differing only by

*the*reversal ... We establish that if H is a triangle-free

*graph*with minimum degree at least k, and

*the*

*graph*obtained by contracting

*the*edges

*of*a matching in H is k-

*connected*, then H is k-

*connected*. ... We are especially grateful to Paul Edelman for pointing out

*the*relationship between

*acyclic*

*orientations*and polytopes, supplying

*the*references, and leading us through

*the*argument described in

*the*appendix ...

##
###
Notes on acyclic orientations and the shelling lemma

2001
*
Theoretical Computer Science
*

In this paper we study two lemmas on

doi:10.1016/s0304-3975(00)00226-7
fatcat:px5qrtcsmvalnkqt7hdfykbzce
*acyclic**orientations*and totally cyclic*orientations**of*a*graph*, which can be derived from*the*shelling lemma in vector subspaces. ... We give simple*graph*theoretical proofs as well as a proof by*the*interpretations*of**the*shelling lemma in*the*special setting*of**graphs*. ...*Connectivity**of**acyclic*ip*graph*) . Let G be a*connected**graph*with n nodes. Then*the**acyclic*ip*graph*is (n − 1)*connected*; and has a vertex*of*degree (n − 1). ...##
###
Acyclic Orientation of Drawings

2010
*
Journal of Graph Algorithms and Applications
*

Given a set

doi:10.7155/jgaa.00211
fatcat:4fk2jsnbwzhhvlyxehxbhfqpz4
*of*curves in*the*plane or a topological*graph*, we ask for an*orientation**of**the*curves or edges which induces an*acyclic**orientation*on*the*corresponding planar map. ... Depending on*the*maximum number*of*crossings on a curve or an edge, we provide algorithms and hardness proofs for this problem. ... We thank Michel Pocchiola for suggesting*the*problem concerning*the**acyclicity**of*curves in*the*plane. We also thank Scot Drysdale, Frank Hoffmann, and Klaus Kriegel for helpful discussions. ...##
###
Acyclic Orientation of Drawings
[chapter]

2006
*
Lecture Notes in Computer Science
*

Given a set

doi:10.1007/11785293_26
fatcat:upsfqgawmredvinesfkmaf7nte
*of*curves in*the*plane or a topological*graph*, we ask for an*orientation**of**the*curves or edges which induces an*acyclic**orientation*on*the*corresponding planar map. ... Depending on*the*maximum number*of*crossings on a curve or an edge, we provide algorithms and hardness proofs for this problem. ... We thank Michel Pocchiola for suggesting*the*problem concerning*the**acyclicity**of*curves in*the*plane. We also thank Scot Drysdale, Frank Hoffmann, and Klaus Kriegel for helpful discussions. ...##
###
Enumerating degree sequences in digraphs and a cycle–cocycle reversing system

2007
*
European journal of combinatorics (Print)
*

We give some new enumerations

doi:10.1016/j.ejc.2005.11.006
fatcat:fklpixdmana3zjtyaival64vtu
*of*indegree sequences*of**orientations**of*a*graph*using*the*Tutte polynomial. ... In particular, concerning*the*cycle-cocycle reversing system, we show that its configurations are in bijection with indegree sequences*of**orientations*having a given vertex (quasi-sink*of**the*system) reachable ...*The*set*of*in-sequences*of**acyclic**orientations**of*a*graph*G is in bijection with*the*set*of**acyclic**orientations**of*G. Proof. ...##
###
Sampling and Counting Acyclic Orientations in Chordal Graphs (Student Abstract)

2022
*
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
*

For a given undirected

doi:10.1609/aaai.v36i11.21667
fatcat:6oz5dsg5djcbvl7ckuk22w5j3u
*graph*, an*acyclic**orientation*is an assignment*of*directions to all*of*its edges which makes*the*resulting directed*graph*cycle-free. ... Counting*of**acyclic**orientations**of*a given chordal*graph*can be done in polynomial time, but*the*previously known techniques do not seem to lead to a corresponding (efficient) sampler. ... Future Plans We view this work as a first step in*the*direction*of*counting and sampling different types*of**graph**orientations*on chordal*graphs*, such as bipolar*orientations*, sink-free*orientations*, and ...##
###
Every Orientation of a $4$-Chromatic Graph has a Non-Bipartite Acyclic Subgraph

2022
*
Electronic Journal of Combinatorics
*

Let $f(n)$ denote

doi:10.37236/10727
fatcat:5ztkwahiancwzodxsbno3vuwhe
*the*smallest integer such that every directed*graph*with chromatic number larger than $f(n)$ contains an*acyclic*subgraph with chromatic number larger than $n$. ...*The*problem*of*bounding this function was introduced by Addario-Berry et al., who noted that $f(n) \leqslant n^2$. ... Suppose G is a*graph**of*chromatic number 4. Then every*orientation**of*its edges contains an*acyclic*odd cycle. ...##
###
Full orientability of graphs with at most one dependent arc

2009
*
Discrete Applied Mathematics
*

Let d min (G) (d max (G)) denote

doi:10.1016/j.dam.2009.04.013
fatcat:laypq2jbqfbcvgqw3rdopobouu
*the*minimum (maximum)*of**the*number*of*dependent arcs over all*acyclic**orientations**of*G. ... Suppose that D is an*acyclic**orientation**of*a*graph*G. An arc*of*D is dependent if its reversal creates a directed cycle. ... Acknowledgments*The*authors would like to thank*the*anonymous referees for their constructive comments. ...##
###
Acyclic orientations of complete bipartite graphs

1995
*
Discrete Mathematics
*

For a complete bipartite

doi:10.1016/0012-365x(94)00222-5
fatcat:fhdk6bygznaa5fel4dbo2edrky
*graph*,*the*number*of*dependent edges in an*acyclic**orientation*can be any integer from n-1 to e, where n and e are*the*number*of*vertices and edges in*the**graph*. ... Acknowledgement*The*author thanks Paul Edelman for communicating*the*problem, Albert Li for interesting discussions about it, and a referee for suggesting stronger versions*of**the*Lemmas. ... Every*acyclic**orientation**of*a*connected*simple*graph*G contains among its independent edges a spanning tree*of*G. Proof. ...##
###
Moving to Extremal Graph Parameters
[article]

2013
*
arXiv
*
pre-print

In this paper we develop a technique which provides answers for several different parameters:

arXiv:1307.5781v1
fatcat:mzplvihkwrazdfwqqrits4vnqu
*the*numbers*of*edges in*the*line*graph*,*acyclic**orientations*, cliques, and forests. ... Which*graphs*, in*the*class*of*all*graphs*with given numbers n and m*of*edges and vertices respectively, minimizes or maximizes*the*value*of*some*graph*parameter? ... Observe that an*acyclic**orientation**of*a*graph*defines an ordering on*the*vertices*of**the**graph*. For a clique this is a bijection. ...##
###
Page 8488 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

Given a chordal bridgeless

*connected*undirected*graph*G,*the*authors construct a linear time algorithm that finds a strongly*connected**orientation**of*G with*oriented*diameter at most one plus twice*the*... During*the*last quarter century considerable work has followed on obtaining strongly*connected**orientations**of**connected*bridgeless*graphs*that minimize*the**oriented*diameter, particularly on special classes ...##
###
On the Broadcast Routing Problem in Computer Networks
[article]

2020
*
arXiv
*
pre-print

Given an undirected

arXiv:1802.08955v3
fatcat:a6pvq25jc5e7hbzvsfkjoffj7y
*graph*G = (V, E), and a vertex r∈ V, an r-*acyclic**orientation**of*G is an*orientation*OE*of**the*edges*of*G such that*the*digraph OG = (V, OE) is*acyclic*and r is*the*unique vertex with ... For w∈R^E_+, k(G, w) is*the*value*of**the*w-maximum packing*of*r-arborescences for all r∈ V and all r-*acyclic**orientations*OE*of*G. ... Future investigations can be studying*the*running time complexity*of*BRP and rBRP in general*graphs*and solve them in larger classes than outerplanar*graphs*. ...##
###
A Proof-checking Experiment on Representing Graphs as Membership Digraphs

2013
*
Italian Conference on Computational Logic
*

These results will be enhanced in a forthcoming scenario, where every

dblp:conf/cilc/CalligarisOT13
fatcat:upyb2wf3t5hpdpukdknl4pwzde
*connected*claw-free*graph*G will receive an extensional*acyclic**orientation*and will, through such an*orientation*, be represented as ... We likewise proved that a*graph*whatsoever admits a weakly extensional and*acyclic**orientation*; consequently, and in view*of*what precedes, one can regard its edges as membership arcs, each deprived*of*... This eases things: for, any vertex with fewer than 2 incident edges in*the*spanning tree*of*a*connected**graph*will be a non-cut vertex*of**the**graph*. Fig. 2 . 2 Fig. 2. ...##
###
Page 6198 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

Summary: “Given a

*graph*G,*the**acyclic**orientation**graph**of*G, denoted AO(G), is*the**graph*whose vertices are*the**acyclic**orientations**of*G, with two*acyclic**orientations*joined by an edge in AO(G) iff ... We also give examples*of**graphs*whose*acyclic**orientation**graph*is not Hamiltonian. ...##
###
The Prism of the Acyclic Orientation Graph is Hamiltonian

1995
*
Electronic Journal of Combinatorics
*

Every

doi:10.37236/1199
fatcat:zum26xlh3rc7dlqtw63dsxccte
*connected*simple*graph*$G$ has an*acyclic**orientation*. ... Define a*graph*${AO}(G)$ whose vertices are*the**acyclic**orientations**of*$G$ and whose edges join*orientations*that differ by reversing*the*direction*of*a single edge. ... Introduction Every*connected*simple*graph*G has an*acyclic**orientation*. ...
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