Some Non-Existence Results on Leech Trees

Hua Wang

Some Non-Existence Results on Leech Trees

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

 More than 25 years ago John Leech posed the following beautiful problem: find, whenever possible, trees on n vertices with positive weights on the edges, such that the (n/2) weighted distances among the n vertices are exactly the number 1, 2, 3, ..., (n/2).
 
 Herbert Taylor gave a proof restricting the number of vertices on which Leech trees can exist to n2 and n2+2. We prove two theorems, giving restrictions on the longest path and maximum degree in Leech trees. We also prove a computer search showing that there is no Leech tree for n =9, 11.

Original language	American English
State	Published - Jan 5 2005
Event	Joint Mathematics Meetings (JMM) - Duration: Jan 6 2017 → …

Conference

Conference	Joint Mathematics Meetings (JMM)
Period	01/6/17 → …

Keywords

Leech trees
Non-existence results

DC Disciplines

Mathematics

Cite this

@conference{11b11468e48d45d3baa39dbe171d7be4,

title = "Some Non-Existence Results on Leech Trees",

abstract = " More than 25 years ago John Leech posed the following beautiful problem: find, whenever possible, trees on n vertices with positive weights on the edges, such that the (n/2) weighted distances among the n vertices are exactly the number 1, 2, 3, ..., (n/2). Herbert Taylor gave a proof restricting the number of vertices on which Leech trees can exist to n2 and n2+2. We prove two theorems, giving restrictions on the longest path and maximum degree in Leech trees. We also prove a computer search showing that there is no Leech tree for n =9, 11.",

keywords = "Leech trees, Non-existence results",

author = "Hua Wang",

year = "2005",

month = jan,

day = "5",

language = "American English",

note = "Joint Mathematics Meetings (JMM) ; Conference date: 06-01-2017",

}

TY - CONF

T1 - Some Non-Existence Results on Leech Trees

AU - Wang, Hua

PY - 2005/1/5

Y1 - 2005/1/5

N2 - More than 25 years ago John Leech posed the following beautiful problem: find, whenever possible, trees on n vertices with positive weights on the edges, such that the (n/2) weighted distances among the n vertices are exactly the number 1, 2, 3, ..., (n/2). Herbert Taylor gave a proof restricting the number of vertices on which Leech trees can exist to n2 and n2+2. We prove two theorems, giving restrictions on the longest path and maximum degree in Leech trees. We also prove a computer search showing that there is no Leech tree for n =9, 11.

AB - More than 25 years ago John Leech posed the following beautiful problem: find, whenever possible, trees on n vertices with positive weights on the edges, such that the (n/2) weighted distances among the n vertices are exactly the number 1, 2, 3, ..., (n/2). Herbert Taylor gave a proof restricting the number of vertices on which Leech trees can exist to n2 and n2+2. We prove two theorems, giving restrictions on the longest path and maximum degree in Leech trees. We also prove a computer search showing that there is no Leech tree for n =9, 11.

KW - Leech trees

KW - Non-existence results

UR - http://jointmathematicsmeetings.org/meetings/national/jmm/2091_abstracts/1003-x1-257.pdf

M3 - Presentation

T2 - Joint Mathematics Meetings (JMM)

Y2 - 6 January 2017

ER -

Some Non-Existence Results on Leech Trees

Abstract

Conference

Keywords

DC Disciplines

Other files and links

Fingerprint

Cite this