1. Spanning k -Ended Tree in 2-Connected Graph.
- Author
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Lei, Wanpeng and Yin, Jun
- Subjects
- *
TREE graphs , *SPANNING trees , *INDEPENDENT sets , *GRAPH connectivity - Abstract
Win proved a very famous conclusion that states the graph G with connectivity κ (G) , independence number α (G) and α (G) ≤ κ (G) + k − 1 (k ≥ 2) contains a spanning k-ended tree. This means that there exists a spanning tree with at most k leaves. In this paper, we strengthen the Win theorem to the following: Let G be a simple 2-connected graph such that | V (G) | ≥ 2 κ (G) + k , α (G) ≤ κ (G) + k (k ≥ 2) and the number of maximum independent sets of cardinality κ + k is at most n − 2 κ − k + 1 . Then, either G contains a spanning k-ended tree or a subgraph of K κ ∨ ((k + κ − 1) K 1 ∪ K n − 2 κ − k + 1) . [ABSTRACT FROM AUTHOR]
- Published
- 2023
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