Partitioning $\alpha $–large sets: Some lower bounds

Partitioning Α–large Sets: Some Lower Bounds

Let α → (β)m denote the property: if A is an α–large set of natural numbers and [A]r is partitioned into m parts, then there exists a β– large subset of A which is homogeneous for this partition. Here the notion of largeness is in the sense of the so–called Hardy hierarchy. We give a lower bound for α in terms of β,m, r for some specific β. This paper is a continuation of our work [2] and [3] o...

Some Lower Bounds for Estrada Index

Some Geometric Lower Bounds

Dobkin and Lipton introduced the connected components argument to prove lower bounds in the linear decision tree model for membership problems, for example the element uniqueness problem. In this paper we apply the same idea to obtain lower bound statements for a variety of problems, each having the avor of element uniqueness. In fact one of these problems is a parametric version of element uni...

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

some lower bounds for estrada index