Results 11 to 20 of about 34,637 (273)
Extremal infinite graph theory
Discrete Mathematics, 2011 We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.
Maya Stein
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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 an extremal problem in graph theory [PDF]
Colloquium Mathematicum, 1964 Let \(l\) and \(p\) be integers such that \(l>p\). It is shown that there exists a constant \(\gamma_{p,l}\) such that if \(n>n_0(p,l)\) then every graph with \(n\) vertices and \([\gamma_{p,l}n^{2-1/p}]\) edges contains a subgraph \(H\) with the following property: the vertices of \(H\) may be labbeled \(x_1,...,x_l\) and \(y_1,...,y_l\) so that every
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Three conjectures in extremal spectral graph theory
Journal of Combinatorial Theory, Series B, 2017 We prove three conjectures regarding the maximization of spectral invariants over certain families of graphs. Our most difficult result is that the join of $P_2$ and $P_{n-2}$ is the unique graph of maximum spectral radius over all planar graphs. This was conjectured by Boots and Royle in 1991 and independently by Cao and Vince in 1993.
Tait, Michael, Tobin, Josh
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A note on the Ramsey numbers for theta graphs versus the wheel of order 5
AKCE International Journal of Graphs and Combinatorics, 2018 The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat +3 more
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, 2020 We study the uniqueness of optimal solutions to extremal graph theory problems. Lovasz conjectured that every finite feasible set of subgraph density constraints can be extended further by a finite set of density constraints so that the resulting set is ...
Grzesik, Andrzej +2 more
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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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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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Guessing Numbers and Extremal Graph Theory
The Electronic Journal of Combinatorics, 2022 For a given number of colors, $s$, the guessing number of a graph is the (base $s$) logarithm of the cardinality of the largest family of colorings of the vertex set of the graph such that the color of each vertex can be determined from the colors of the vertices in its neighborhood.
Martin, Jo, Rombach, Puck
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On new results on extremal graph theory, theory of algebraic graphs, and their applications
Доповiдi Нацiональної академiї наук України, 2022 New explicit constructions of infinite families of finite small world graphs of large girth with well-defined projective limits which is an infinite tree are described.
V.O. Ustimenko
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