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Showing 1 to 20 of 34 for “"Digraphs"”.
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Maximally connected graphs and digraphs
The graph theoretical parameter edge-connectivity equals the minimum number of edges, whose removal disconnects the graph. Analogously, the vertex-connectivity equals the minimum number of vertices, whose removal disconnects the graph. These parameters are maximal, if they are equal to the minimum …
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Minors and planar embeddings of digraphs
… local rotation at each vertex. Clustered planar digraphs have planar embeddings in which, at each vertex, all of the in-arcs occur sequentially in the local rotation. Three different variations of minors are presented, each of which produces a finite set of obstructions to clustered planarity. …
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Choice Functions, Digraphs, and Balanced Allocations
In this thesis, we consider broadly the concept of choice in a variety of settings, focusing on equity in selection. In particular, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges, and are interested, for instance, in minimal numbers …
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D-colorable digraphs with large girth
… in a digraph setting.</p> <p>Let C and D be digraphs. A mapping f:V(D)&rarr V(C) is a C-coloring if for every arc uv of D, either f(u)f(v) is an arc of C or f(u)=f(v), and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colorable if it admits a …
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D-colorable digraphs with large girth
… in a digraph setting.</p> <p>Let C and D be digraphs. A mapping f:V(D)&rarr V(C) is a C-coloring if for every arc uv of D, either f(u)f(v) is an arc of C or f(u)=f(v), and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colorable if it admits a …
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Intersection representations of graphs and digraphs
A digraph is an interval digraph if each vertex can be assigned a source interval and a sink interval on the real line such that there is an edge from u to v if and only if the source interval for u intersects the sink interval for v. A digraph is an indifference digraph or unit interval digraph if …
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K-ordered graphs and out-arc pancyclicity on digraphs
… an important branch of graph theory, the area of digraphs has developed enormously within the last four decades. There are large numbers of topics on digraphs. Out-arc pancyclicity is one of the newest and most interesting themes on digraphs, which deals with the existence of the vertices whose …
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Extremal problems for labelling of graphs and distance in digraphs
… in graph labelling and in weak diameter of digraphs. In Chapter 2 we apply the Discharging Method to prove the 1,2,3-Conjecture [41] and the 1,2-Conjecture [48] for graphs with maximum average degree less than 8/3. Stronger results on these conjectures have been proved, but this is the first …
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Packings and Coverings of Various Complete Digraphs with the Orientations of a 4-Cycle.
… are given for covering complete directed digraphs <em>D<sub>v</sub></em>, packing and covering complete bipartite digraphs, <em>D<sub>m,n</sub></em>, and packing and covering the complete digraph on <em>v</em> vertices with hole of size <em>w</em>, <em>D</em>(<em>v</em>,<em>w</em>), with …
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Exact covering system digraphs a number-theoretic family of directed graphs on the integers
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms
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Decomposition, Packings and Coverings of Complete Digraphs with a Transitive-Triple and a Pendant Arc.
<p>In the study of design theory, there are eight orientations of the complete graph on three vertices with a pendant edge, <em>K</em><sub>3</sub>∪{<em>e</em>}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient …
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Ádám's Conjecture and Arc Reversal Problems
… and identify structure common to all digraphs for which Ádám's conjecture holds. We investigate quasi-acyclic digraphs and verify that Ádám's conjecture holds for such digraphs. We develop the notions of arc-cycle transversals and reversal sets to classify and quantify this structure. …
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Cuts and connectivity in graphs and hypergraphs
… cut and connectivity problems on graphs, digraphs, hypergraphs and hedgegraphs. The main results are the following: - We introduce a faster algorithm for finding the reduced graph in element-connectivity computations. We also show its application to node separation. - We present several …
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Problems in the Theory of Convergence Spaces
… convergence spaces, representation of reflexive digraphs as convergence spaces, construction of differential calculi on convergence spaces, mereology on convergence spaces, and construction of a universal homogeneous pretopological space. First, we generalize Kolmogorov separation from …
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Machine learning and combinatorial methods for discrete optimization problems
… will focus on unsplittable flow problems in digraphs. We begin with the integer and unsplittable multiflow problem in series-parallel digraphs. An unsplittable multiflow routes the demand for each commodity along a single path from its source to its sink node. As one of our main results, we …
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A methodology for the identification of critical locations in infrastructures
… models the infrastructures as interconnected digraphs and employs graph theory and reliability theory to identify the vulnerable points. The vulnerable points are screened for their susceptibility to a terrorist attack, and a prioritized list of critical locations is produced. The …
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Interaction graphs derived from activation functions and their application to gene regulation
… is related to a natural transformation of signed digraphs called switching isomorphism. This is a useful tool for the analysis of interaction graphs used throughout the rest of the dissertation.</p> <p>We then discuss the question of what restrictions, if any, apply to interaction graphs derived …
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