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On edge transitivity of directed graphs

Jayme L. Szwarcfiter
1995 Discrete Mathematics  
We examine edge transitivity of directed graphs. The class of local comparability graphs is defined as the underlying graphs of locally edge transitive digraphs.  ...  Finally, a new characterization of circle graphs is given also in terms of edge transitivity.  ...  Introduction We examine a special orientation of an undirected graph, called locally edge transitive, a generalization of edge transitive orientation.  ... 
doi:10.1016/0012-365x(93)e0182-4 fatcat:yvkkcpsmzja7bc6is7oz6byoum

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

Ilkyoo Choi, Jinha Kim, Minki Kim
2018 arXiv   pre-print
can be executed on the graph while preserving the semi-transitive orientability.  ...  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.  ...  For every transitive orientation φ of a complete graph K , the directed graph φ(K ) has exactly one source and exactly one sink. Suppose K is a complete graph of order at least 4.  ... 
arXiv:1810.11620v1 fatcat:wxbwrlsy4nelnfgdila5ul7tj4

Weakly transitive orientations, Hasse diagrams and string graphs

Matthias Middendorf, Frank Pfeiffer
1993 Discrete Mathematics  
Pfeiffer, Weakly transitive orientations, Hasse diagrams and string graphs, Discrete Mathematics  ...  Nesetiil for a stimulating introduction to the topic of string graphs.  ...  For an acyclically oriented graph G, we call an edge rs of the (undirected) complete graph on the vertex set of G transitive with respect to G if G contains a directed path between the vertices Y and s  ... 
doi:10.1016/0012-365x(93)90176-t fatcat:nj2otqqsjndvzkq4drshug64l4

Dynamic shortest paths and transitive closure: Algorithmic techniques and data structures

Camil Demetrescu, Giuseppe F. Italiano
2006 Journal of Discrete Algorithms  
This is an annotated bibliography on fully dynamic algorithms for path problems on general directed graphs.  ...  Although research on these problems spans over more than three decades, in the last couple of years many novel algorithmic techniques have been proposed. *  ...  In the fully dynamic transitive closure problem we wish to maintain a directed graph G = (V, E) under an intermixed sequence of the following operations: Insert(x, y): insert an edge from x to y; Delete  ... 
doi:10.1016/j.jda.2005.12.003 fatcat:dyr5qbndajfqzlppmiojqhen4e

What must be contained in every oriented k-uniform hypergraph

P Frankl
1986 Discrete Mathematics  
Since H is strongly transitive, the directed graph H,~ is transitive. Let il, i2, • .. , in be a permutation of 1, ..., n so that all directed edges in H,~ go from left to right.  ...  Frankl edge by a transitive tournament ordered according to the permutation :r-~ph then take the union of these directed edges. Definition 2.  ... 
doi:10.1016/0012-365x(86)90219-0 fatcat:5myamom5hrhyza6tvou3xjc36m

Transitive digraphs with more than one end

Norbert Seifter
2008 Discrete Mathematics  
On the other hand all known examples of digraphs with more than one end are either highly arc transitive or at most 1-arc transitive.  ...  For undirected graphs with these properties it has been shown that they are trees as soon as they are 2-arc transitive. In the case of digraphs the situation is much more involved.  ...  The thin ends are all directed and consist of single directed infinite paths which contain exactly one edge of each copy of L 0 such a path meets.  ... 
doi:10.1016/j.disc.2007.04.011 fatcat:7i2wzlhyzra4df5cqwyvq7ul6e

Non-normal edge-transitive directed Cayley graphs of abelian groups

Mehdi Alaeiyan, Javad Mirzajani
2013 Mathematical Sciences  
For a group G, and a subset S of G such that 1 G ∈ S, let X = Cay(G, S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if N Aut(X) (G) is transitive on edges.  ...  In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal.  ...  Authors' contributions MA and JM carried out the algebraic graph theory studies together and both of them participated in each part of this paper. Both authors read and approved the final manuscript.  ... 
doi:10.1186/2251-7456-7-7 fatcat:lzjsaosh7bdjdgell55bzfddti

Detecting hierarchical structure in molecular characteristics of disease using transitive approximations of directed graphs

Juby Jacob, Marcel Jentsch, Dennis Kostka, Stefan Bentink, Rainer Spang
2008 Computer applications in the biosciences : CABIOS  
By good transitive approximation we understand transitive graphs, which differ from the reference graph in only a small number of edges.  ...  In the core of our modeling approach lies the problem of calculating good transitive approximations of given directed but not necessarily transitive graphs.  ...  D.K. was supported by the Deutsche Krebshilfe in the context of the Molecular Mechanisms in Malignant Lymphomas Network Project.  ... 
doi:10.1093/bioinformatics/btn056 pmid:18285370 fatcat:xo2qzgbjvfddzc75v3up3k2xc4

Transitive graphs uniquely determined by their local structure

Joshua Frisch, Omer Tamuz
2015 Proceedings of the American Mathematical Society  
We show that the "grandfather graph" has the following property: it is the unique completion to a transitive graph of a large enough finite subgraph of itself.  ...  While all vertices in a transitive graph are isomorphic, not all directed edges are necessarily isomorphic. Figure 2 . The ball of radius one in the grandfather graph G 3 .  ...  Then each vertex has a unique edge in the direction of this end. Call the vertex on the other side of that edge the "father".  ... 
doi:10.1090/proc/12901 fatcat:venv3i5vuvbnpij6ggmngufcre

Peking: Profiling Syntactic Tree Parsing Techniques for Semantic Graph Parsing

Yantao Du, Fan Zhang, Weiwei Sun, Xiaojun Wan
2014 Proceedings of the 8th International Workshop on Semantic Evaluation (SemEval 2014)  
Using the SemEval-2014 Task 8 data, we profile the syntactic tree parsing techniques for semantic graph parsing.  ...  Evaluation gauges how successful data-driven dependency graph parsing can be by applying existing techniques.  ...  Depth-first-search We try graph traversal by depth-first-search starting from the root on the directed graph ignoring the direction of edges.  ... 
doi:10.3115/v1/s14-2080 dblp:conf/semeval/DuZSW14 fatcat:hiwtjhlxjjfxbcwks7dxjiy3wq

On semi-transitive orientability of Kneser graphs and their complements [article]

Sergey Kitaev, Akira Saito
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.  ...  Also, we show computationally that a subgraph S on 16 vertices and 36 edges of K(8,3), and thus K(8,3) itself on 56 vertices and 280 edges, is non-semi-transitive.  ...  Acknowledgment We are grateful to Li-Da Tong for raising our interest in Kneser graphs.  ... 
arXiv:1903.02777v1 fatcat:dmx732q3zjbabdmfvifk5d3h6y

Asymmetric Transitivity Preserving Graph Embedding

Mingdong Ou, Peng Cui, Jian Pei, Ziwei Zhang, Wenwu Zhu
2016 Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '16  
Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v.  ...  The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs.  ...  Can we straightforwardly apply undirected graph embedding methods on directed graphs? The answer is no due to a fundamentally different characteristic of directed graphs: asymmetric transitivity.  ... 
doi:10.1145/2939672.2939751 dblp:conf/kdd/OuCPZ016 fatcat:qrhtrbyvlbbrvf53fdbcso3p7a

Solving computational problems in the theory of word-representable graphs [article]

Özgür Akgün, Ian P. Gent, Sergey Kitaev, Hans Zantema
2018 arXiv   pre-print
Our computational results in this paper not only include distribution of k-representable graphs on at most 9 vertices, but also have relevance to a known conjecture on these graphs.  ...  Word-representable graphs generalize several important classes of graphs. A graph is word-representable iff it admits a semi-transitive orientation.  ...  A semi-cycle is the directed acyclic graph obtained by reversing the direction of one edge of a directed cycle in which the directions form a directed path.  ... 
arXiv:1808.01215v1 fatcat:yzl3vjtnajce3jxyi2g4nxwyna

Balanced Non-Transitive Dice II: Tournaments [article]

Alex Schaefer
2017 arXiv   pre-print
We then show how to construct a set of n dice such that the relation behaves according to the direction of the arrows of any tournament (complete directed graph) on n vertices.  ...  We further study sets of labeled dice in which the relation "is a better die than" is non-transitive.  ...  A directed graph G is realizble by a set of dice D if there is a one-to-one map f : D → V (G) such that P (A ≻ B) > 1 2 implies that (f (A), f (B)) is a directed edge of G.  ... 
arXiv:1706.08986v1 fatcat:jsree66d65ehpmvbm4mplippqu

On the Existence of Word-representable Line Graphs of Non-word-representable Graphs [article]

M M Akbar, P D Akrobotu, C P Brewer
2021 arXiv   pre-print
This results in an example where the line graph of a non-word-representable graph is both 3-semi-transitive and semi-transitive and thus is word-representable.  ...  By formulating an appropriate optimization problem for the decision problem of 3-semi-transitive graphs, we show that the line graph of a non-word-representable graph can be word-representable.  ...  If such a pair is found, then the edge is directed from i to j. • If no such k, m are found, then edge can be oriented in either direction. Then, move on to the next edge.  ... 
arXiv:2108.02363v1 fatcat:5uxpjbtqjrbhfdxeyzz2zuarla
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