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Spanning trees in graphs of minimum degree 4 or 5. (English) Zbl 0776.05031
Summary: For a connected simple graph $$G$$ let $$L(G)$$ denote the maximum number of leaves in any spanning tree of $$G$$. Lineal conjectured that if $$G$$ has $$N$$ vertices and minimum degree $$k$$, then $$L(G)\geq((k-2)/(k+1))N+c_ k$$, where $$c_ k$$ depends on $$k$$. We prove that if $$k=4$$, $$L(G)\geq{2\over 5}N+{8\over 5}$$; if $$k=5$$, $$L(G)\geq{1\over 2}N+2$$. We give examples showing that these bounds are sharp.

##### MSC:
 05C05 Trees 05C35 Extremal problems in graph theory
##### Keywords:
minimum degree; spanning tree; bounds
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##### References:
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