On extremal sizes of locallyk-tree graphs
✍ Scribed by Mieczysław Borowiecki; Piotr Borowiecki; Elżbieta Sidorowicz; Zdzisław Skupień
- Book ID
- 111707667
- Publisher
- Springer
- Year
- 2010
- Tongue
- English
- Weight
- 250 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0011-4642
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📜 SIMILAR VOLUMES
graph with girth no less than 2t + 1 and minimum degree no less than k/t and d(T), then G contains each tree T of size k. It is known that this conjecture holds for t = 1 and t = 2. We prove it in the case t = 3.
A graph G admits a tree-partition of width k if its vertex set can be partitioned into sets of size at most k so that the graph obtained by identifying the vertices in each set of the partition, and then deleting loops and parallel edges, is a forest. In the paper, we characterize the classes of gra
Let T(G) be the tree graph of a graph G with cycle rank r. Then K ( T ( G ) ) 3 m ( G ) -r, where K(T(G)) and m(G) denote the connectivity of T ( G ) and the length of a minimum cycle basis for G, respectively. Moreover, the lower bound of m ( G ) -r is best possible.