##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 641.05046

**Autor: ** Alavi, Yousef; Boals, Alfred J.; Chartrand, Gary; Erdös, Paul; Oellermann, Ortrud R.

**Title: ** The ascending subgraph decomposition problem. (In English)

**Source: ** Combinatorics, graph theory, and computing, Proc. 18th Southeast. Conf., Boca Raton/Fl. 1987, Congr. Numerantium 58, 7-14 (1987).

**Review: ** [For the entire collection see Zbl 638.00009.]

Let G be a graph of positive size q, and let n be that positive integer for which \binom{n+1}{2} \leq q < \binom{n+2}{2}. Then G is said to have an ascending subgraph decomposition if G can be decomposed into n subgraphs G_{1},G_{2},...,G_{n} without isolated vertices such that G_{i} is isomorphic to a proper subgraph of G_{i+1} for 1 \leq i \leq n-1. Several classes of graphs possessing an ascending subgraph decomposition are described.

**Classif.: ** * 05C70 Factorization, etc.

**Keywords: ** ascending subgraph decomposition

**Citations: ** Zbl 638.00009

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag