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Decompositions into two paths

100%

Skupień Z.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 3

325-329

It is proved that a connected multigraph G which is the union of two edge-disjoint paths has another decomposition into two paths with the same set, U, of endvertices provided that the multigraph is neither a path nor cycle. Moreover, then the number of such decompositions is proved to be even unless the number is three, which occurs exactly if G is a tree homeomorphic with graph of either symbol + or ⊥. A multigraph on n vertices with exactly two traceable pairs is constructed for each n ≥ 3. The Thomason result on hamiltonian pairs is used and is proved to be sharp.

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1 Discussiones Mathematicae Graph Theory

1 Skupień Z.

1 2005

Wyniki wyszukiwania

Decompositions into two paths