Anna Moraht- Fromm, Gerhard Weilandt (Hrsgg.), Unter der Lupe. Neue Forschungen zu Skulptur und Malerei des Hoch- Spätmittelalters. Festschrift für Hans Westhoff zum 60 Geburtstag, Stuttgart/Ulm (Thorbecke, Süddeutsche Verlagsgesellschaft) 2000. 352 S., zahlr. Abb.

This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.

An antimagic labeling of a graph G with m edges is a bijection from E(G) to {1, 2, . . . ,m} such that for all vertices u and v, the sum of labels on edges incident to u differs from that for edges incident to v. Hartsfield and Ringel conjectured that every connected graph other than the single edge K2 has an antimagic labeling. We prove this conjecture for regular graphs of odd degree.

A k-uniform hypergraphH = (V ;E) is said to be self-complementary whenever it is isomorphic with its complement H = (V ; ` V k ́ −E). Every permutation σ of the set V such that σ(e) is an edge ofH if and only if e ∈ E is called selfcomplementing. 2-self-comlementary hypergraphs are exactly self complementary graphs introduced independently by Ringel (1963) and Sachs (1962). For any positive inte...

For a tree T , the graph X is T -decomposable if there exists a partition of the edge set of X into isomorphic copies of T . In 1963, Ringel conjectured that K2m+1 can be decomposed by any tree with m edges. Graham and Häggkvist conjectured more generally that every 2m-regular graph can be decomposed by any tree with m edges. Fink showed in 1994 that for any directed tree T with m arcs, the dir...