On k l Leaf Powers 1st Edition by Andreas Brandstadt, Peter Wagner ISBN 9783540744566

On (k,ℓ)-Leaf Powers 1st Edition by Andreas Brandstadt, Peter Wagner – Ebook PDF Instant Download/Delivery. 9783540744566
Full download On (k,ℓ)-Leaf Powers 1st Edition after payment

Product details:

ISBN 10: 
ISBN 13: 9783540744566
Author: Andreas Brandstadt, Peter Wagner

We say that, for k ≥ 2 and ℓ> k, a tree T is a (k,ℓ)-leaf root of a graph G = (V _G ,E _G ) if V _G is the set of leaves of T, for all edges xy ∈ E _G , the distance d _T (x,y) in T is at most k and, for all non-edges <span id="MathJax-Element-1-Frame" class="MathJax_SVG" style="box-sizing: inherit; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 18px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="xy∉EG”>��∉��, d _T (x,y) is at least ℓ. A graph G is a (k,ℓ)-leaf power if it has a (k,ℓ)-leaf root. This new notion modifies the concept of k-leaf power which was introduced and studied by Nishimura, Ragde and Thilikos motivated by the search for underlying phylogenetic trees. Recently, a lot of work has been done on k-leaf powers and roots as well as on their variants phylogenetic roots and Steiner roots. For k = 3 and k = 4, structural characterisations and linear time recognition algorithms of k-leaf powers are known, and, recently, a polynomial time recognition of 5-leaf powers was given. For larger k, the recognition problem is open.

We give structural characterisations of (k,ℓ)-leaf powers, for some k and ℓ, which also imply an efficient recognition of these classes, and in this way we also improve and extend a recent paper by Kennedy, Lin and Yan on strictly chordal graphs and leaf powers.

On (k,ℓ)-Leaf Powers 1st Table of contents:

People also search for On (k,ℓ)-Leaf Powers 1st:

on (k,ℓ)-leaf powers 1st
    
1 leaf
    
l.k.1.b
    
l.k.1.d
    
l.k.1e