Essays in extremal combinatorics

Extremal Combinatorics: with Applications in Computer Science by Stasys Jukna, Springer, 2001, xvii + 375 pp

Short Proofs of Some Extremal Results

We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because in each case the relevant proofs are quite short.

On the extremal total irregularity index of n-vertex trees with fixed maximum degree

In the extension of irregularity indices, Abdo et. al. [1] defined the total irregu-larity of a graph G = (V, E) as irrt(G) = 21 Pu,v∈V (G) du − dv, where du denotesthe vertex degree of a vertex u ∈ V (G). In this paper, we investigate the totalirregularity of trees with bounded maximal degree Δ and state integer linear pro-gramming problem which gives standard information about extremal trees a...

Turán - type Problems in Extremal Combinatorics Adam Marcus

Methods and Challenges in Extremal and Probabilistic Combinatorics∗ Organizers

Combinatorics, or discrete mathematics, is a fundamental mathematical discipline, concerned with the study of discrete mathematical objects such as graphs, set families and permutations, their typical and extremal properties, and their enumeration. A natural mathematical framework for a large variety of human activities and endeavors, combinatorics has been in existence for thousands of years. ...