Two graphs G and H are hypomorphic if there exists a bijection φ : V (G)→ V (H) such that G− v ∼= H − φ(v) for each v ∈ V (G). A graph G is reconstructible if H ∼= G for all H hypomorphic to G. It is well known that not all infinite graphs are reconstructible. However, the Harary-Schwenk-Scott Conjecture from 1972 suggests that all locally finite trees are reconstructible. In this paper, we con...

This report, including an abundance of tables, describes in detail various experiments designed to throw light on problems encountered in the Japanese program of producing BCG vaccine for immunization against tuberculosis. Studies were made of production of dried vaccine, of methods of preservation, of virulence, and of potency in guinea pigs. Discussion follows the description of each experime...

This is a survey paper illuminating the distinguished role of the Mittag-Leffler function and its generalizations in fractional analysis and fractional modeling. The content of the paper is connected to the recently published monograph by Rudolf Gorenflo, Anatoly Kilbas, Francesco Mainardi and Sergei Rogosin.

Suppose a graph G = (V, E) with edge weights w(e) and edges partitioned into disjoint categories S1, . . . , Sp is given. We consider optimization problems P on G defined by a family of feasible sets D(G) and the following objective function: L5(D) = max 1≤i≤p ( max e∈Si∩D w(e)− min e∈Si∩D w(e) ) For an arbitrary number of categories we show that the L5-perfect matching, L5-a-b path, L5-spannin...

Generalizing the well-known theorem of Halin (1964) that a countable connected graph G contains an end-faithful spanning tree (i.e., an end-preserving tree that omits no end of G), we establish some results about the existence of end-preserving spanning trees omitting some prescribed set of ends. We remark that if such a tree exists, the omitted ends must all be dominated, and even then counter...

Thomassen introduced the concept of a finitely spreading graph: an infinite graph whose edges can be oriented, each in one, both, or neither direction, so that every vertex has finite out-degree and every ray has a forward oriented tail. He conjectured that a graph is finitely spreading if and only if it is bounded in the sense of Halin—equivalently (see [5]), if it contains none of three speci...

In order to solve a problem arising when generalizing topographical maps, we consider the following problem for simple polygons, i.e., coherent polygons without holes. Some edges of the polygon may be marked as hard, and at least two vertices of the polygon are marked as terminals. We show that the problem to nd a tree of minimum total length, spanning the hard edges and terminals, using only e...

We define treetopes, a generalization of the threedimensional roofless polyhedra (Halin graphs) to arbitrary dimensions. Like roofless polyhedra, treetopes have a designated base facet such that every face of dimension greater than one intersects the base in more than one point. We prove an equivalent characterization of the 4-treetopes using the concept of clustered planarity from graph drawin...