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 29 for “"minimum degree"”.
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On the δ-conjecture for graphs with minimum degree |G| – 4
For a graph G of order n, the minimum rank of G is defined to be the minimum rank among all n × n symmetric matrices whose ij-entry is nonzero precisely when {i, j} is an edge of G. The delta conjecture proposes a relationship between the minimum rank and the minimum degree of a given graph. We …
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Independent Domination Of Subcubic Graphs
… The independent domination number i(G) is the minimum cardinality among all maximal independent sets of G. A graph is subcubic whenever the maximum degree is at most three. In this paper, we will show that the independent domination number of a connected subcubic graph of order n having minimum …
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Sufficient degree conditions for graph embeddings
… showed a sufficient bound involving maximum degrees, and this was further explored by Kaul and Kostochka to characterize all extremal cases. Bollobas and Eldridge (and independently Sauer and Spencer) developed edge sum bounds to guarantee packing. In Chapter 2, we introduce the new idea of …
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On cycles in directed graphs
… 0 every sufficiently large oriented graph G with minimum indegree and minimum outdegree at least 3 |G| / 8 + alpha |G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen. Furthermore, answering completely a conjecture of Haggkvist and Thomason, we show that we …
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Chords of longest circuits of graphs
… graph G has a chord if G is cubic or if the minimum degree is at least 4. In 1997, Carsten Thomassen proved that every longest circuit of 3-connected cubic graph has a chord.;In this dissertation, we prove the following three independent partial results: (1) Every longest circuit of a …
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Cliques in graphs
… of $r$-cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a triangle-free graph of order $n$ has at most $n^2/4$ edges. Hence, a triangle-free graph has minimum degree at most $n/2$, so if $k_3(n,\delta) =0$ then $\delta \le n/2$. …
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Chromatic Thresholds of Regular Graphs with Small Cliques
… such that any graph in this class with a minimum degree greater than <em>θn</em> has a bounded chromatic number. Several important results related to the chromatic threshold of triangle-free graphs have been reached in the last 13 years, culminating in a result by Brandt and Thomassé …
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The regularity method in directed graphs and hypergraphs
… any k-uniform hypergraph on n vertices with minimum degree at least \(\frac{n}{\lceil k / (k - \ell) \rceil (k - \ell)}\) + o(n) contains a Hamilton \(\ell\)-cycle. This result confirms a conjecture of Han and Schacht, and is best possible up to the o(n) error term. Together with results of …
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The Chromatic Structure of Dense Graphs
… and chromatic number of graphs with large minimum degree and where every neighbourhood is r-colourable? Chapter 3 deals with the locally bipartite case and Chapter 4 with the general case. While the subject of Chapters 3 and 4 is a natural local to global colouring question, it is also …
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Hamiltonian cycles in maximal planar graphs and planar triangulations
… First we discuss maximal planar graphs with minimum degree i, for i = 3; 4; 5, and the subgraph induced by the vertices of G with the same degree. Finally we discuss the connectivity of G, a maximal planar graph with minimum degree i. Chapter 4 will be devoted to Hamiltonian cycles in maximal …
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Improving Separation of Signals from Multiple Physical Quantities Detected by Sensor Arrays
… Cuthill-McKee (SRCM) and Symmetric Approximate Minimum Degree (SAMD) permutations of the coherence matrix.
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Precise Partitions Of Large Graphs
… misbehaving vertices. Furthermore, sharp minimum degree and degree sum conditions are proven for the existance of a Hamiltonian cycle passing through specified vertices with prescribed distances between them in large graphs. Finally, we prove a sharp connectivity and degree sum condition …
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The Characterization Of Graphs With Small Bicycle Spectrum
… bicircular matroids whose associated graphs have minimum degree at least i for k ≥ 1, and show that there exists a set of bicycles with consecutive bicycle lengths.
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A linear multigrid preconditioner for the solution of the Navier-Stokes equations using a discontinuous Galerkin discretization
… (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill-Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and a novel algorithm is presented for the application of the linearization which reduces both the memory and CPU time …
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Problems of optimal choice on posets and generalizations of acyclic colourings
… number of a graph as functions of its maximum degree. I shall begin Chapter 1 by describing the classical secretary problem, in which the aim is to select the best candidate for the post of a secretary, and its solution. I shall then summarize some of its many generalizations that have been …
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Extremal and Structural Problems of Graphs
… proper edge colouring of a graph of maximum degree $\Delta$ be extended to a proper colouring of the entire graph using an `optimal' set of colours? Albertson and Moore conjectured this is always possible provided no two precoloured edges are within distance $2$. The main result of …
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A Comparison of the Effects of Two Adult Cardiovascular Education Approaches on Risk Reduction Behaviors of Adults and Their Children
… education programs is the determination of the minimum degree of personal instruction needed to give maximum yield from mass media at the lowest possible cost. The present research provides an assessment of amount of individual contact necessary to provide maximum results to inner-city minority …
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Proper connection number of graphs
… constructing classes of 2-connected graphs with minimum degree $\delta(G)\geq3$ that have proper connection number 3. Furthermore, we study sufficient conditions in terms of the ratio between the minimum degree and the order of a 2-connected graph $G$ implying that $G$ has proper connection …
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From narcotrafficking to alternative governance: An ethnographic study on Los Caballeros Templarios and the mutation of organized crime in Michoacán, Mexico
… to organized crime. The group perceived a minimum degree of legitimacy as crucial to control over locally rooted resources and thus survival. I argue that this drove the construction of a project of alternative governance; in essence a ceremonially enacted narrative portraying LCT as a …
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An Evolutionary Approach to Solving the Maximum Size Consecutive Ones Submatrix and Related Problems
… insertion approach. Moreover, preprocessing by minimum degree ordering is also used. On the other hand, we suggest another approach to solve the C1S. It is using the MVEE problem. To pave the way we first solve the problem. Given a set of points C = {x 1 ,x 2 ,...,x m } ⊆ R^n , what is the …
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