Let G be a connected graph on n ≥ 2 vertices with girth at least g such that the length of a maximal chain of successively adjacent vertices of degree 2 in G does not exceed k ≥ 1. Denote by u(G) the maximum number of leaves in a spanning tree of G. We prove that u(G) ≥ αg,k(υ(G) − k − 2) + 2 where αg,1=[g+12]4[g+12]+1 and αg,k=12k+2 for k ≥ 2. We present an infinite series of examples showing that all these bounds are tight.
Original language | English |
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Pages (from-to) | 36-43 |
Number of pages | 8 |
Journal | Journal of Mathematical Sciences (United States) |
Volume | 232 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jul 2018 |
Externally published | Yes |
ID: 36924996