For a graph G and its spanning tree T the backbone chromatic number, BBC(G,T ), is defined as the minimum k such that there exists a coloring c : V (G) → {1, 2, . . . , k} satisfying |c(u) − c(v)| ≥ 1 if uv ∈ E(G) and |c(u)− c(v)| ≥ 2 if uv ∈ E(T ). Broersma et al. [1] asked whether there exists a constant c such that for every triangle-free graphG with an arbitrary spanning tree T the inequali...

In 1992, A. Ehrenfeucht and J. Mycielski defined a seemingly pseuorandom binary sequence which has since been termed the EM-sequence. The balance conjecture for the EM-sequence, still open, is the conjecture that the sequence of EM-sequence initial segment averages converges to 1=2. In this paper, we do not prove the balance conjecture but we do make some progress concerning it, namely, we prov...

Assume 〈א0,א1〉 → 〈λ, λ +〉. Assume M is a model of a first order theory T of cardinality at most λ+ in a vocabulary L(T ) of cardinality ≤ λ. Let N be a model with the same vocabulary. Let ∆ be a set of first order formulas in L(T ) and let D be a regular filter on λ. Then M is ∆-embeddable into the reduced power N /D, provided that every ∆-existential formula true in M is true also in N . We ob...

Inspired by Fagin’s result that NP = Σ11, we have developed a partial framework to investigate expressibility inside Σ11 so as to have a finer look into NP . The framework uses interesting combinatorics derived from second-order Ehrenfeucht-Fräıssé games and the notion of game types. Some of the results that have been proven within this framework are: (1) for any k, divisibility by k is not exp...

This paper gives a sufficient condition for a graph G to have its circular chromatic number equal its chromatic number. By using this result, we prove that for any integer t ≥ 1, there exists an integer n such that for all k ≥ n χc(M (Kk)) = χ(M (Kk)).

Wind speed modeling and prediction plays a critical role in wind related engineering studies. However, since the data have random behavior, it is difficult to apply statistical approaches with apriori and deterministic parameters. On the other hand, wind speed data have an important feature; extreme transitions from a wind state to a far different one are rare. Therefore, behavioral modeling is...

We investigate some topological properties of a normal functor H introduced earlier by Radul which is a certain functorial compactification of the HartmanMycielski construction HM . We show that H is open and find the condition when HX is an absolute retract homeomorphic to the Tychonov cube.