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The swelling of natural porous materials, including bleached pulp, as represented by mathematical descriptions, is influenced by a variety of different operating factors. The formerly used Generalised Hygroscopicity Model leads to either a disproportion between a model and a limit value of the sorption capacity or to noticeable deviation in the early swelling phase. Alternatively, the so-called Simple Bounded Growth model solely depends on the maximum sorption capacity, ignoring the physical properties that affect the fibre swelling rate. This research shows that the combination of the two models best describes the swelling process of bleached pulp -a rapid swelling phase and a slower swelling phase. The combined model was found to be useful in characterizing the well-known hornification process.

The concepts of critical and cocritical radius edge-invariant graphs are introduced. We prove that every graph can be embedded as an induced subgraph of a critical or cocritical radius-edge-invariant graph. We show that every cocritical radius-edge-invariant graph of radius r ≥ 15 must have at least 3r + 2 vertices.

ABSTRACT. The eccentricity e(v) of vertex v is defined as a distance to a farthest vertex from v. The radius of a graph G is defined as r(G) = minWe consider properties of unchanging the radius of a graph under two different situations: deleting an arbitrary edge and deleting an arbitrary vertex. This paper gives the upper bounds for the number of edges in such graphs.

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.