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Showing 1 to 5 of 5 for “"graph minors"”.
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Graph minors and algorithms
A graph H is a minor of another graph G, denoted by $H\ {\prec\sb{m}}\ G,$ if a graph isomorphic to H can be obtained from G by a series of vertex deletions, edge deletions, and edge contractions. Graph minors have been studied for several decades as a way of characterizing classes of graphs. …
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Extremal Theory of Graph Minors and Related Topics
… tight bounds for the maximum average degree of a graph with no H minor for several new classes of graph H. Chapter 2 derives an upper bound for almost all graphs H with t vertices and average degree d for a new sparse regime with d = t^o(1). Chapter 3 extends these results to use additional …
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Extremal graph theory: Ramsey-Turán numbers, chromatic thresholds, and minors
… investigates several questions in extremal graph theory and the theory of graph minors. It consists of three independent parts; the first two parts focus on questions motivated by Turan's Theorem and the third part investigates a problem related to Hadwiger's Conjecture. Let H be a graph, t …
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Excluding a Weakly 4-connected Minor
A 3-connected graph $G$ is called weakly 4-connected if min $(|E(G_1)|, |E(G_2)|) \leq 4$ holds for all 3-separations $(G_1,G_2)$ of $G$. A 3-connected graph $G$ is called quasi 4-connected if min $(|V(G_1)|, |V(G_2)|) \leq 4$. We first discuss how to decompose a 3-connected graph into quasi …
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Tightening curves and graphs on surfaces
… homotopy moves and a set of local operations on graphs called electrical transformations. Electrical transformations have been used to simplify electrical networks since the 19th century; later they have been used for solving various combinatorial problems on graphs, as well as applications in …