The following assertions are shown to be equivalent, for any countable graph G: (1) G can be represented as the intersection graph of a family of subtrees of a tree; (2) G admits a tree-decomposition (Robertson/Seymour) into primes; (3) G is chordal, and G admits a simpkial tree-decomposition (Halin
Clique-sums, tree-decompositions and compactness
✍ Scribed by Igor Kříž; Robin Thomas
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 588 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
We develop a technique
for extending excluded minor theorems to infinite graphs, and in particular we answer a question of Neil Robertson.
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