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An Orientation Theorem for Graphs

1994
*
Journal of combinatorial theory. Series B (Print)
*

We characterize the class of

doi:10.1006/jctb.1994.1064
fatcat:u4qp44dwfjcitasfo7fmosyuwi
*graphs*in which the edges can be*oriented*in such a way that going along any circuit in the*graph*, the number of forward edges minus the number of backward edges is equal to ... The result follows by applying Tutte's characterization of regular matroids to a certain binary matroid associated to a*graph*. irj ... ACKNOWLEDGMENT I thank Andras Frank and Alexander Schrijver*for*stimulating discussions. ...##
###
Simultaneous well-balanced orientations of graphs

2006
*
Journal of combinatorial theory. Series B (Print)
*

Nash-Williams' well-balanced

doi:10.1016/j.jctb.2006.01.002
fatcat:fg2ll64zsrh5lexjpxufzkz6mu
*orientation**theorem*[11] is extended*for**orienting*several*graphs*simultaneously. ... We also have new results about simultaneous well-balanced*orientations*of non-disjoint subgraphs of*an*Eulerian*graph*as well as those of different contractions of a*graph*. ... Acknowledgement We thank András Frank*for*many helpful discussions. ...##
###
Orientations of graphs

2010
*
Matemática contemporânea
*

We provide here a short survey on

doi:10.21711/231766362010/rmc3919
fatcat:iu7kjo4cvfh5hlg2hqokipmpwe
*orientations*of*graphs*. We concentrate on problems with connectivity properties. ... It is known that this is true*for*Eulerian*graphs*[1]:*Theorem*7.1 (Berg-Jordán). ...*For*every partition {V 1 , . . . V k } of V (G), there exists*an**orientation*G of G such that G and G/V i ∀i, are best-balanced*orientations*of the corresponding*graphs*. ...##
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On ordered graphs and graph orderings

1994
*
Discrete Applied Mathematics
*

A

doi:10.1016/0166-218x(94)90100-7
fatcat:4ahyds76snd3bf47jeyyjzo7ry
*graph*H is said to have the ordering property*for*(G, d ) if*for*every ordered*graph*(H, 5) (i.e.*for*every linear ordering 3 of vertices of H) there exists*an*induced subgraph G' = (V, E') such that ... In this note we discuss various existential problems related to*graph**orientations*, to ordered*graphs*and their relationship to Ramsey theory. ... (d):*for*every ordered*graph*(G, < ), G E Forb(d) there exists*an*ordered*graph*(H, < ), H E Forb(d) such that (H, <) + (G, <)t. (3)*Oriented*Ramsey*Theorem**for*Forb(d):*For*every acyclic*orientation*G ...##
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Oriented graph coloring

2001
*
Discrete Mathematics
*

*An*

*oriented*k-coloring of

*an*

*oriented*

*graph*G (that is a digraph with no cycle of length 2) is a partition of its vertex set into k subsets such that (i) no two adjacent vertices belong to the same subset ... We survey the main results that have been obtained on

*oriented*

*graph*colorings. ...

*An*

*oriented*

*graph*is then nice if it is n-nice

*for*some n. More precisely, we have [17] :

*Theorem*14 (NeÄ setÄ ril et al. [17] ). ...

##
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A dualistic approach to bounding the chromatic number of a graph

2008
*
European journal of combinatorics (Print)
*

We exhibit infinitely many examples where this general setting improves the bounds

doi:10.1016/j.ejc.2003.09.024
fatcat:z47caqab2zegjc3bvca463olia
*for*chromatic number of*graphs*and we relate this to extremal problems*for**oriented**graphs*. ... We give a new and more direct proof of the characterization*theorem**for*finitary homomorphism dualities of directed*graphs*. ... This research was done while the second author was visiting the Institute*for*Theoretical Computer Science (ITI) in the fall of 2000. The support of DIMATIA is gratefully acknowledged. ...##
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A survey on the skew energy of oriented graphs
[article]

2015
*
arXiv
*
pre-print

Let G^σ be

arXiv:1304.5707v6
fatcat:gwbwrvdqmfeuzky3lfguczkdjm
*an**oriented**graph*of G with skew adjacency matrix S(G^σ). ... In this paper, we summarize main results on the skew energy of*oriented**graphs*. Some open problems are proposed*for*further study. ... It is almost sure that*for*every*graph*G, the energy of G is less than the skew energy of*an**oriented**graph*G σ of G.*Theorem*9.4. ...##
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Dualities and reciprocities on graphs on surfaces
[article]

2021
*
arXiv
*
pre-print

We extend the duality between acyclic

arXiv:2005.01590v2
fatcat:ubsujef37jccbh7nj5bdgfhyz4
*orientations*and totally cyclic*orientations*on planar*graphs*to dualities on*graphs*on*orientable*surfaces by introducing boundary acyclic*orientations*and totally ... In addition, we provide a reciprocity*theorem*connecting local tensions and boundary acyclic*orientations*. ... In this subsection, we provide a reciprocity*theorem**for*integral local tension as follows.*Theorem*4.11. Let G be*an**oriented**graph*on a surface. ...##
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Antisymmetric flows and strong colourings of oriented graphs

1999
*
Annales de l'Institut Fourier
*

-Every bridgeless

doi:10.5802/aif.1705
fatcat:a47kgkyqz5hgxj7yqvlcsldwl4
*graph*G has*an**orientation**for*wich G has a Zy-ASF (i.e. asf^(G') < 7*for*every bridgeless*graph*G). Proof. -By Seymour's*theorem*[25] , any bridgeless*graph*has a Z2 x Zs-NZF. ... We shall give several proofs of the fact that*an*ASF exists*for*any*oriented**graph*without*oriented*2-cut. ...##
###
Eigenvalues of oriented-graph matrices

1995
*
Linear Algebra and its Applications
*

We give bounds on the real and imaginary parts of the eigenvalues of

doi:10.1016/0024-3795(93)00233-p
fatcat:ad57nunjrzgcfjvu5kf7stnmby
*an**oriented*-*graph*matrix, prove that each of the irreducible*oriented*-*graph*matrices of order n 2 3 has at least three distinct eigenvalues ... We also consider spectral properties of the bipartite*oriented*-*graph*matrices and the multiequipartite*oriented*-*graph*matrices. ...*For*the imaginary parts of the eigenvalues of*an**oriented*-*graph*matrix, we have*THEOREM*2.4. ...##
###
Orientations of infinite graphs
[article]

2021
*
arXiv
*
pre-print

Building on recent work by Thomassen, we show that Nash-Williams'

arXiv:2011.05936v2
fatcat:5quvowxp2vhunkmftsjgph3szi
*orientation**theorem*, that every finite 2k-edge-connected multigraph has a k-arc-connected*orientation*, also holds*for*all infinite multigraphs ... Nash-Williams'*orientation**theorem**for*infinite*graphs*We are now ready to extend Nash-Williams'*orientation**theorem*to all infinite multigraphs. ... Thomassen proved in [12,*Theorem*4 ] that*for*any finite set of vertices A 0 in a 4k-edge-connected locally finite*graph*G, there is*an*immersion in G of a finite Eulerian 2k-edge-connected*graph*on A ...##
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Context Directed Reversals and the Ciliate Decryptome
[article]

2016
*
arXiv
*
pre-print

The cds Rescue

arXiv:1603.06149v3
fatcat:hnheua3hezgrfbkhczmytpx7lq
*Theorem*is discussed in the context of a mathematical model*for*ciliate micronuclear decryption. ... cdr Parity*Theorem*). ... Acknowledgements The research represented in this paper was funded by*an*NSF REU grant DMS 1359425, by Boise State University and by the Department of Mathematics at Boise State University. ...##
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A note on ''The comparability graph of a tree"

1965
*
Proceedings of the American Mathematical Society
*

We say that a relation T on G is

doi:10.1090/s0002-9939-1965-0172274-5
fatcat:pjinnjr4svajvcofphkj5zvye4
*an**orientation*of (G, R) if and only if (i) (G, T) is*an**oriented**graph*, and (ii) x R y if and only if x T y or y T x,*for*all x, y EG. ...*An*unoriented*graph*which possesses a transitive*orientation*will be called a comparability*graph*. ...##
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On semi-transitive orientability of Kneser graphs and their complements
[article]

2019
*
arXiv
*
pre-print

*An*

*orientation*of a

*graph*is semi-transitive if it is acyclic, and

*for*any directed path v_0→ v_1→...→ v_k either there is no edge between v_0 and v_k, or v_i→ v_j is

*an*edge

*for*all 0≤ i<j≤ k. ...

*An*undirected

*graph*is semi-transitive if it admits a semi-transitive

*orientation*. ... Acknowledgment We are grateful to Li-Da Tong

*for*raising our interest in Kneser

*graphs*. ...

##
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On operations preserving semi-transitive orientability of graphs
[article]

2018
*
arXiv
*
pre-print

Moreover,

arXiv:1810.11620v1
fatcat:wxbwrlsy4nelnfgdila5ul7tj4
*for*all three*graph*operations,we showthat the initial semi-transitive*orientation*can be extended to the new*graph*obtained by the*graph*operation. ... We consider the class of semi-transitively*orientable**graphs*, which is a much larger class of*graphs*compared to transitively*orientable**graphs*, in other words, comparability*graphs*. ... By*Theorem*1.11, it is enough to show*Theorem*1.12*for*edge-deletions.*Theorem*2.2. Let e be*an*edge of a semi-transitively*orientable**graph*G . ...
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