Extremal problems of Chebyshev type

Extremal graph packing problems: Ore-type versus Dirac-type

We discuss recent progress and unsolved problems concerning extremal graph packing, emphasizing connections between Dirac-type and Ore-type problems. Extra attention is paid to coloring, and especially equitable coloring, of graphs.

Extremal Problems for Geometric Hypergraphs 1 Extremal Problems for Geometric

A geometric hypergraph H is a collection of i-dimensional simplices, called hyperedges or, simply, edges, induced by some (i + 1)-tuples of a vertex set V in general position in d-space. The topological structure of geometric graphs, i.e., the case d = 2; i = 1, has been studied extensively, and it proved to be instrumental for the solution of a wide range of problems in combinatorial and compu...

Extremal Graph Problems, Degenerate Extremal Problems, and Supersaturated Graphs

Notation. Given a graph, hypergraph Gn, . . . , the upper index always denotes the number of vertices, e(G), v(G) and χ(G) denote the number of edges, vertices and the chromatic number of G respectively. Given a family L of graphs, hypergraphs, ex(n,L) denotes the maximum number of edges (hyperedges) a graph (hypergraph)Gn of order n can have without containing subgraphs (subhypergraphs) from L...

Turán - type Problems in Extremal Combinatorics Adam Marcus

Carathéodory-Fejér type extremal problems on locally compact Abelian groups

We consider the extremal problem of maximizing a point value | f (z) | at a given point z ∈ G by some positive definite and continuous function f on a locally compact Abelian group (LCA group) G, where for a given symmetric open set Ω ∋ z, f vanishes outside Ω and is normalized by f (0) = 1. This extremal problem was investigated in R and Rd and for Ω a 0-symmetric convex body in a paper of Boa...