Global ETD Search
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Showing 1 to 8 of 8 for “"Disjoint cycles"”.
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Extremal problems in disjoint cycles and graph saturation
… for the existence of a given number of disjoint cycles in a graph. Further, our refined theorem leads to an answer for a question posed by G. Dirac in 1963 regarding the existence of disjoint cycles in graphs with a certain connectivity. This answer comprises Chapter 3. In Chapter 4 we …
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Sufficient degree conditions for graph embeddings
… 3, we discuss the problem of finding k vertex-disjoint cycles in a multigraph. This problem originated from a conjecture of Erdos and has led to many different results. Corradi and Hajnal looked at a minimum degree condition. Enomoto and Wang independently looked at a minimum degree-sum …
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The Element Spectrum Of A Graph
… of graphs and matroids that have cycles or circuits of specified cardinality have been given by authors including Edmonds, Junior, Lemos, Murty, Reid, Young, and Wu. In particular, a matroid with circuits of a single cardinality is called a Matroid Design. We consider a …
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Cyclic, f-Cyclic, and Bicyclic Decompositions of the Complete Graph into the 4-Cycle with a Pendant Edge.
… the complete graph on <em>v</em> vertices into 4-cycles with a pendant edge. In part, we will consider decompositions which admit automorphisms consisting of:</p><p>(1) a single cycle of length <em>v</em>,</p><p>(2) <em>f</em> fixed points and a cycle of length <em>v</em> − <em>f</em>, …
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Sufficient conditions for the existence of specified subgraphs in graphs
… 1963 that considers when a graph contains many disjoint cycles. Generalizing the seminal result of Corrádi and Hajnal, they prove that if a graph G contains many more vertices of degree at least 2k than vertices of degree at most 2k-2, then G contains k vertex-disjoint cycles. We strengthen …
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The Configuration Space of Two Particles Moving on a Graph
… space. We develop an intersection theory for cycles in graphs inspired by the classical intersection theory for cycles in manifolds and we use this to develop an algorithm to calculate the second Betti number of F (Γ,2) for any graph Γ. We also use this intersection theory to provide a …
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Discrepancy Inequalities in Graphs and Their Applications
… of similar questions about the number of vertex-disjoint subgraphs of a certain class that a graph with some degree condition must contain. While this problem is well-studied for dense graphs, many results give significantly worse bounds for less dense graphs. Using spectral graph theory, we show …
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Linear Orderings of Sparse Graphs
… the dual problem of Feedback Arc Set, the Arc-Disjoint Cycles problem.