内容提示: Extremal Graph TheoryPo-Shen LohJune 2009Extremal graph theory, in its strictest sense, is a branch of graph theory developed and loved byHungarians.(The opening sentence in Extremal Graph Theory, by B´ ela Bollob´ as.)1Warm-up1. What is the smallest possible number of ...
Extremal Graph Theorydoi:10.1007/978-3-662-70107-2_7In this chapter we study how global parameters of a graph, such as its edge density or chromatic number, can influence its local substructures.Diestel, ReinhardUniversität HamburgSpringer, Berlin, Heidelberg...
Based on my lecture given there, I shall survey those parts of Extremal Graph Theory that are connected most directly with Paul Erdős’s work. In Turán type extremal problems we usually have some sample graphs L1,…,Lr, and consider a graph G n on n vertices not containing any L i ...
Part II Graph Theory, lectured by Julian Sahasrabudhe Part III Combinatorics, lectured by Béla Bollobás Part III Extremal and Probabilistic Combinatorics, lectured by Julian Sahasrabudhe The target The formal system which we are using as a target system is Lean's dependent type theory. Lean is...
For a graph F, let exr(n,F) denote the maximum number of hyperedges in an r-uniform hypergraph on n vertices which does not contain a Berge-F as a subgraph. The case when r=2 is the classical Turán function ex(n,F). We will also consider what happens if we impose the additional...
European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2009) Edited by Jaroslav Nešetřil, André Raspaud Other articles from this issue Chip-Firing, Antimatroids, and Polyhedra 1 August 2009 Kolja Knauer View PDF On the Sumset Partition Problem 1 August 2009 A. Lladó...
extremal graph theoryLet κl denote the complete graph on l vertices. We prove that there is a constant c = c(l) > 0, such that whenever p ≥ n-c, with probability tending to 1 when n goes to infinity, every maximum κl-free subgraph of the binomial random graph Gn, p is (l-...
Journal of Graph TheoryM.Knor, J.S˘ira´n˘, Extremal graphs of diameter two and given maximum degree, embed- dable in a fixed surface, J. Graph Theory, 24 (1997) No. 1, 1-8.M. Knor and J. Sˇira´nˇ, Extremal graphs of diameter two and given maximum degree, ...
Trinajstić, Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17, 535–538 (1972) Article Google Scholar Z. Gu, S. Zhou, J. Liu, Q. Zhou, D. Wang, Shapley distance and Shapley index for some special graphs. Parallel Process...
Mantel’s Theorem from 1907 [21] is one of the foundational results in extremal graph theory. It asserts that a triangle-free graphGonnvertices has at most\lfloor \frac{n^2}{4}\rflooredges, with equality if and only ifGis (isomorphic to) the complete balanced bipartite graphT_2(n)....