Results 31 to 40 of about 34,637 (273)
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
Brualdi, Richard A., Mellendorf, Stephen
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A ramsey-type theorem for multiple disjoint copies of induced subgraphs
Discussiones Mathematicae Graph Theory, 2014 Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to ...
Nakamigawa Tomoki
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General Multiplicative Zagreb Indices of Graphs With Bridges
IEEE Access, 2020 Multiplicative Zagreb indices have been studied due to their extensive applications. They play a substantial role in chemistry, pharmaceutical sciences, materials science and engineering, because we can correlate them with numerous physico-chemical ...
Monther Rashed Alfuraidan +3 more
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Horizontal Visibility graphs generated by type-I intermittency [PDF]
, 2013 The type-I intermittency route to (or out of) chaos is investigated within the Horizontal Visibility graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct, according ...
Gómez, José Patricio +4 more
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Tur\'an Graphs, Stability Number, and Fibonacci Index
, 2008 The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and ...
A. Knopfmacher +20 more
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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.
Erdős, Paul, Simonovits, M.
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Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Discussiones Mathematicae Graph Theory, 2015 It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima +2 more
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On the maximum orders of an induced forest, an induced tree, and a stable set [PDF]
Yugoslav Journal of Operations Research, 2014 Let G be a connected graph, n the order of G, and f (resp. t) the maximum order of an induced forest (resp. tree) in G. We show that f - t is at most n - 2√n-1. In the special case where n is of the form a2 + 1 for some even integer a ≥ 4, f -
Hertz Alain +2 more
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, 2014 Positional games are a branch of combinatorics, researching a variety of two-player games, ranging from popular recreational games such as Tic-Tac-Toe and Hex, to purely abstract games played on graphs and hypergraphs.
Krivelevich, Michael
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An extremal problem in graph theory [PDF]
Journal of the Australian Mathematical Society, 1970 G(n;l) will denote a graph of n vertices and l edges. Let f0(n, k) be the smallest integer such that there is a G (n;f0(n, k)) in which for every set of k vertices there is a vertex joined to each of these. Thus for example fo = 3 since in a triangle each pair of vertices is joined to a third.
Erdős, Pál, Moser, L.
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