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Some problems in extremal graph theory and finite geometry
, 2023 This thesis is devoted to the study of several problems in extremal graph theory and finite geometry. We study properties such as girth, spectrum, and automorphism group of various families of algebraically defined graphs. We present a new and shorter proof of the girth of the family of graphs D(n, q). We also determine the asymptotics of the number of
Taranchuk, Vladislav
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An extremal problem in graph theory
Israel Journal of Mathematics, 1968It is proved that the maximum number of cut-vertices in a connected graph withn vertices andm edges is $$max\left\{ {q:m \leqq (_2^{n - q} ) + q} \right\}$$ All the extremal graphs are determined and the corresponding problem for cut-edges is also solved.
A Ramachandra Rao
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Extremal problems in graph theory
Journal of Graph Theory, 1977AbstractThe aim of this note is to give an account of some recent results and state a number of conjectures concerning extremal properties of graphs.
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On some extremal problems in graph theory
Israel Journal of Mathematics, 1965Der Verf. beweist, daß für eine genügend große Konstante \(c\) jeder Graph \(G\) mit \(n\) Punkten und \(cn^{3/2}\) Kanten ein Sechseck \(x_1,x_2,x_3,x_4,x_5,x_6\) enthält und dazu noch einen siebenten Punkt \(y\), der mit \(x_1,x_3\) und \(x_5\) verbunden ist.
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Extremal graph theory and finite forcibility [PDF]
Electronic Notes in Discrete Mathematics, 2017 We study the uniqueness of optimal solutions to extremal graph theory problems. Our main result is a counterexample to the following conjecture of Lov´asz, which is often referred to as saying that “every extremal graph theory problem has a finitely ...
Daniel Kral +2 more
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