## Halving complete 4-partite graphs.(English)Zbl 0994.05117

Factor of a graph $$G$$ is a subgraph of $$G$$ containing each vertex of $$G$$. Factors of $$G$$ are said to form a decomposition of $$G$$ if their edge sets partition the edge set of $$G$$.
The authors completely determine the spectrum (i.e. set of orders) of complete 4-partite graphs with at most one odd part which are decomposable into two isomorphic factors with a finite diameter. For complete 4-partite graphs with all parts odd the authors solve the spectrum problem completely for factors with diameter 5 and partially for the remaining possible finite diameters (2, 3, and 4).
This problem was solved earlier by P. Híc and D. Palumbíny for complete graphs [Math. Slovaca 37, 247-254 (1987; Zbl 0675.05051)], and by D. Fronček for complete bipartite and tripartite graphs [Graphs Comb. 12, 305-320 (1996; Zbl 0866.05050)].

### MSC:

 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

### Citations:

Zbl 0675.05051; Zbl 0866.05050