A Note on Extremal Combinatorics of Cyclic Split Systems
نویسنده
چکیده
It is shown that every cyclic split system S defined on an n-set with #S > 2kn− (2k+1 2 ) for some k ≤ n−1 2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k, n−(2k+1)) ≤ 3. In addition, some related old and new conjectures are also discussed.
منابع مشابه
Extremal Results in Random Graphs
According to Paul Erdős [Some notes on Turán’s mathematical work, J. Approx. Theory 29 (1980), page 4] it was Paul Turán who “created the area of extremal problems in graph theory”. However, without a doubt, Paul Erdős popularized extremal combinatorics, by his many contributions to the field, his numerous questions and conjectures, and his influence on discrete mathematicians in Hungary and al...
متن کاملTopics in Extremal Combinatorics - Notes
3 Lecture 3 8 3.1 Krivelevich’s proof that r(3, k) ≥ ck2/ log k . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Ajtai-Komlós-Szemerédi’s r(3, k) < ck2/ log k . . . . . . . . . . . . . . . . . . . . . . 9 3.3 AKS Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 AKS formal proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملOn 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...
متن کاملTransient Two-Dimensional (r-z) Cyclic Charging/Discharging Analysis of Space Thermal Energy Storage Systems (RESEARCH NOTE)
A two-dimensional transient axi-symmetric model was developed to study the effects of various thermal and geometric parameters on cyclic heating and cooling modes of a phase-change thermal energy storage system. The high-temperature thermal energy storage device utilizes LiH for heat sink applications to store the waste heat generated during power-burst periods. The stored heat is then discharg...
متن کاملA note on the zeroth-order general randić index of cacti and polyomino chains
The present note is devoted to establish some extremal results for the zeroth-order general Randi'{c} index of cacti, characterize the extremal polyomino chains with respect to the aforementioned index, and hence to generalize two already reported results.
متن کامل