Let T be a tree with n vertices. Let k be the maximum degree of a vertex of T. Let lbe the length of the longest path in T. Prove thatl ≤ n − k +1.

Step 1:Definitions and Setup:T is a tree with n vertices.k is the maximum degree of a vertex in T,…

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

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Let T be a tree with n vertices. Let k be the maximum degree of a vertex of T. Let l be the length of the longest path in T. Prove that l ≤ n − k +1.