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A property of trees in terms of unique connected subgraphs

✍ Scribed by Stephen T. Hedetniemi; Diane M. Spresser

Book ID
102340845
Publisher
John Wiley and Sons
Year
1977
Tongue
English
Weight
116 KB
Volume
1
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The following theorem is proved: Let G be a graph with p β‰₯ 3 points such that for some n, 3 ≀ n ≀ p, any n points lie on a unique smallest connected subgraph. Then G = C~n~+1 or G is a tree, and conversely.

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Various Hamiltonian-like properties are investigated in the squares of connected graphs free of some set of forbidden subgraphs. The star K,+ the subdivision graph of &, and the subdivision graph of K1,3 minus an endvertex play central roles. In particular, we show that connected graphs free of the