Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 30 for “"Perfect matching"”.
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Excluding Two Minors of the Petersen Graph
… graph created by contracting three edges of a perfect matching of the Petersen Graph. In Chapter 3, we determine the structure of any large internally 4-connected graph which has no P_2 minor, where P_2 is a graph on 8 vertices, 13 edges, and is isomorphic to the graph created by contracting …
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The induced path number of complementary prisms
… G and its complement G by adding the edges of a perfect matching between the corresponding vertices of G and G. The induced path number, denoted ρ(G), of a graph G is defined as the minimum number of subsets that the vertex set of G can be partitioned into such that each subset induces a path. In …
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Matching problems in hypergraphs
… choose 2} - {2n/3 choose 2}, then H contains a perfect matching. We show that for sufficiently large n divisible by 3, if F_1, ..., F_{n/3} are 3-uniform hypergraphs with a common vertex set and the minimum vertex degree in each F_i is greater than {(n-1) choose 2} - {2n/3 choose 2} for i = 1, …
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The Structure of 4-Clusters in Fullerenes
… 4 and our models have valence 3, the edges of a perfect matching are doubled to bring the valence up to 4 at each vertex. The edges in this perfect matching are called a Kekule structure and the hexagonal faces bounded by three Kekule edges are called benzene rings. A maximal independent …
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Independent Domination in Complementary Prisms.
… and <em>G̅</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. For example, if <em>G</em> is a 5-cycle, then <em>GG̅</em> is the Petersen graph. In this paper we investigate independent domination in complementary prisms.</p>
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Phase transition for cutoff for random walks on random graphs
… Given a stochastic matrix Q, we pick a random perfect matching of the half-edges subject to the constraint that each vertex v has degint(v) neighbours inside its community and the proportion of outgoing half-edges from community i matched to a half-edge from community j is Q(i,j). Assuming the …
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Double Domination of Complementary Prisms.
… and its complement <em>G̅</em> by adding a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. For any graph <em>G</em>, a set <em>D</em> ⊆ <em>V</em> (<em>G</em>) is a <em>double dominating set</em> (DDS) if that set dominates every vertex of <em>G</em> twice. …
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Circuits, Perfect Matchings and Paths in Graphs
… shall present a series of conjectures related to perfect matching covering and point out their relationship.;In last chapter, we shall introduce the saturation number, in contrast to extremal number (or known as Turan Number), and describe the edge spectrum of saturation number for small paths, …
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Embedding problems in graphs and hypergraphs
The first part of this thesis concerns perfect matchings and their generalisations. We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph, thereby answering a question of Hàn, Person and Schacht. We say that a graph \(G\) has a perfect \(H\)-packing (also …
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Flows, Submodularity, Sparsity, and Beyond: Continuous Optimization Insights for Discrete Problems
… negative-weight shortest path and minimum cost perfect matching. In the second part of the thesis, we investigate efficient optimization algorithms for problems relevant to machine learning that have some discrete element, such as sparse or low rank structure. We introduce a new technique, …
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From String to Structure: Graph Threading for Physical Assembly
… algorithm via reduction to minimum-weight perfect matching, prove tight worst-case bounds on optimal threadings, and identify special cases with faster algorithms. For the turn metric, we characterize the complexity landscape, proving NP-hardness for graphs of maximum degree 4, tractability …
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Locating-Domination in Complementary Prisms.
… and <em>G̅</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em> and <em>G̅</em>. A set <em>D</em> ⊆ <em>V</em> (<em>G</em>) is a locating-dominating set of <em>G</em> if for every <em>u</em> ∈ <em>V</em> (<em>G</em>)<em>D</em>, its neighborhood …
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Accelerating dynamic programming
… such as shortest paths, feasible flow, bipartite perfect matching, and replacement paths can be accelerated by DPs that exploit a total-monotonicity property of the shortest paths. - Combining Compression and Total Monotonicity. We introduce a method for accelerating string edit distance …
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Shortest paths, Markov chains, matrix scaling and beyond : improved algorithms through the lens of continuous optimization
… with negative weights and minimum cost bipartite perfect matching problems. In the case of sparse graphs, this provides the first running time improvement for these problems in over 25 years. *-- We initiate the study of solving linear systems involving directed Laplacian matrices, and devise an …
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Intractability Results for some Computational Problems
… Multilinear Boolean Circuits for Bipartite Perfect Matching: A monotone Boolean circuit is said to be multilinear if for any AND gate in the circuit, the minimal representation of the two input functions to the gate do not have any variable in common. We show that monotone multilinear …
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Mixing of random walks on random graphs and intersections of branching random walks
… we add edges corresponding to a uniformly chosen perfect matching, assigning weight $\eps_n$ to these edges and weight $1$ to the original edges of $G_n$. In 2020 Hermon, Sly and Sousi~\cite{random_matching} studied this model in the case $\eps_n\equiv1$ and they showed that a random walk on …
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Extremal Problems for Partitions of Edge Sets of Graphs
… girth 9 or higher decomposes into a forest and a matching. We also show that a planar graph that has no cycles of length 4 decomposes into a forest and a graph with maximum degree at most 5. Finally, we prove that the number of perfect matchings in a certain family of planar graphs is divisible by …
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Fast simulation of E1, B1 and Specific Absorption Rate for 7T MRI with the use of graphical processors
… is provided of how FDTD with Uniaxial Perfect Matching Layer (UPML) boundary conditions was coded on GPUs using the NVIDIA CUDA framework. FDTD equations were CUDA optimized by use of two kernel functions, one for the E field update equations and another for the B field update …
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Paired-Domination in Grid Graphs.
… em>-1</sub><em>v</em><sub>2<em>t</em></sub>} is a perfect matching in 〈<em>S</em>〉, the subgraph induced by <em>S</em>. The domination number of a graph <em>G</em> is the smallest cardinality of any dominating set of <em>G</em>, and the paired-domination number is the smallest cardinality of any …
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Extremal, Probabilistic, and Infinitary Problems in Combinatorics
… we are interested in finding a colour-balanced perfect matching within a colour-balanced complete graph K_(2nk) with a palette of k colours. An edge-colouring of a graph G is said to be colour-balanced if there are equally many edges of each available colour. While it is not necessarily possible …
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