an:04149918
Zbl 0701.90092
Satyanarayana, A.; Tung, L.
A characterization of partial 3-trees
EN
Networks 20, No. 3, 299-322 (1990).
00155481
1990
j
90C35 05C05
subgraphs; k-trees; partial 3-tree
The paper is concerned with a class of subgraphs called k-trees and their subgraphs. A k-tree is defined recursively as follows. The complete graph \(K_ k\) on k points is a k-tree. Given a k-tree G on \(n\geq k\) points, a k-tree on \(n+1\) points is obtained by adding a new point u and edges connecting u to every point of a \(K_ k\) in G. A partial k-tree is a subgraph of some k-tree. The authors establish properties of partial 3- trees and show that a graph is a partial 3-tree if and only if it has no subgraph contractible to \(K_ 5\), \(K_{2,2,2}\), \(C_ 8(1,4)\&K_ 2\times C_ 5\). Hitherto, such a characterization of partial k-trees was known only for the values of \(k\leq 2\).
M.Savelsbergh