Results 31 to 40 of about 5,888,750 (277)
Triangles in Ks-saturated graphs with minimum degree t
Theory and Applications of Graphs, 2020 For $n \geq 15$, we prove that the minimum number of triangles in an $n$-vertex $K_4$-saturated graph with minimum degree 4 is exactly $2n-4$, and that there is a unique extremal graph.
Craig Timmons +3 more
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Some problems in extremal graph theory and finite geometry
, 2023 Lazebnik, FelixThis 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
Taranchuk, Vladislav
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On the VC-dimension, covering and separating properties of the cycle and spanning tree hypergraphs of graphs [PDF]
Transactions on Combinatorics, 2022 In this paper, we delve into studying some relations between the structure of the cycles and spanning trees of a graph through the lens of its cycle and spanning tree hypergraphs which are hypergraphs with the edge set of the graph as their vertices ...
Alireza Mofidi
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Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory [PDF]
, 2015 In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph ...
Narayanan, Bhargav
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On the conjunctive capacity of graphs [PDF]
, 2013 The investigation of the asymptotic behaviour of various graph parameters in powers of a fixed graph G=(V,E) is motivated by problems in information theory and extremal ...
Chlebikova, Janka +5 more
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A Unified Approach for Extremal General Exponential Multiplicative Zagreb Indices
Axioms, 2023 The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline ...
Rashad Ismail +4 more
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On a problem in extremal graph theory
Journal of Combinatorial Theory, Series B, 1977 From the authors introduction. Let \(G(n,m)\) denote a graph \((V,E)\) with \(n\) vertices and \(m\) edges and \(K_1\) a complete graph with \(i\) vertices. \textit{P.Turán} proved that every \(G(n,T(n,k))\) contains a \(K_k\), where \[ T(n,k) = \frac{k-2}{2(k-1)}(n^2-r^2)+\binom r2+1, \] \(r\equiv n(\mod k-1)\) and \(0\leq r\leq k-2\).
D. T. Busolini, Paul Erdös
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On the number of pentagons in triangle-free graphs [PDF]
, 2013 Using the formalism of flag algebras, we prove that every triangle-free graph G with n vertices contains at most (n/5)(5) cycles of length five. Moreover, the equality is attained only when n is divisible by five and G is the balanced blow-up of the ...
Hatami, Hamed +4 more
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Two Extremal Problems in Graph Theory
The Electronic Journal of Combinatorics, 1994 We consider the following two problems. (1) Let $t$ and $n$ be positive integers with $n\geq t\geq 2$. Determine the maximum number of edges of a graph of order $n$ that contains neither $K_t$ nor $K_{t,t}$ as a subgraph. (2) Let $r$, $t$ and $n$ be positive integers with $n\geq rt$ and $t\geq 2$. Determine the maximum number of edges of a graph of
Richard A. Brualdi, Stephen Mellendorf
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Compactness results in extremal graph theory [PDF]
Combinatorica, 1982 (From the authors' abstract:) ``Let \(L\) be a given family of \dots 'prohibited graphs'. Let \(\text{ex}(n,L)\) denote the maximum number of edges a simple graph of order n can have without containing subgraphs from \(L\). A typical extremal graph problem is to determine \(\text{ex}(n,L)\), or, at least, to find good bounds on it.
Paul Erdös, Miklós Simonovits
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