Let G be a graph. The vertex edge arboricity of G denoted by a G a1 G is the minimum number of subsets into which the vertex edge set of G can be partitioned so that each subset induces an acyclic subgraph. Let d be a graphical sequence and let R d be the class of realizations of d. We prove that if π ∈ {a, a1}, then there exist integers x π and y π such that d has a realization G with π G z if...

We show that hereditarily indecomposable spaces can be characterized by a special instance of the Intermediate Value Theorem in their ring of continuous functions.

The solvability of nonlinear equations has awakened great interest among mathematicians for a number of centuries, perhaps as early as the Babylonian culture (3000–300 B.C.E.). However, we intend to bring to our attention that some of the problems studied nowadays appear to be amazingly related to the time of Bolzano’s era (1781–1848). Indeed, this Czech mathematician or perhaps philosopher has...

Abstract Let $$\mathfrak {f}= I-k$$ f = I - k be a compact vector field of class $$C^1$$ C 1 on real Hilbert space $$\mathbb {H}$$ H . In the spi...