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 4 of 4 for “"toroidal graphs"”.
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Extremal problems on variations of graph colorings
… we study how forbidding certain structures (subgraphs) affects a given coloring parameter. Open since 1977, the Borodin--Kostochka Conjecture states that given a graph $G$ with maximum degree $\Delta(G)$ at least 9, if $G$ has no clique of size $\Delta(G)$, then $G$ is $(\Delta(G)-1)$-colorable. …
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Results in Ramsey theory and extremal graph theory
… lower bounds on a certain quantity relating to graphs. The first problem is in Ramsey theory, while the others are in extremal graph theory. In Chapter 2, which is joint work with Vojtěch Dvořák, we consider the Ramsey number $R(F_n)$ of the fan graph $F_n$, a graph consisting of $n$ triangles …
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Coloring and covering problems on graphs
… There is no stronger bound even for bipartite graphs, since $\pi_f(K_{m,m})=\pi_f(K_{m+1,m})=\frac{3m}{m+1}$. We also compute $\pi_f(G)$ for cycles and some complete tripartite graphs. We show that $\pi_f(G)<\sqrt{2}$ when $G$ is a tree and present a sequence of trees on which the value tends …
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Equilibrium graphs on the flat torus or finding zen amidst the bull
… spring embedding theorem, and equilibrium graphs on the plane in general, have been a subject of study for many decades, with connections to and applications in many areas, including, but not limited to, discrete geometry, planar graph theory, graphics, surface parametrization, mechanical …