Paper Info
Title
Tight Descriptions of 3-Paths in Normal Plane Maps : Dedicated to Andre Raspaud on the occasion of his 70th birthday.
Abstract
We prove that every normal plane map (NPM) has a path on three vertices (3-path) whose degree sequence is bounded from above by one of the following triplets: (3, 3, ), (3,15,3), (3,10,4), (3,8,5), (4,7,4), (5,5,7), (6,5,6), (3,4,11), (4,4,9), and (6,4,7). This description is tight in the sense that no its parameter can be improved and no term dropped. We also pose a problem of describing all tight descriptions of 3-paths in NPMs and make a modest contribution to it by showing that there exist precisely three one-term descriptions: (5, , 6), (5, 10, ), and (10, 5, ). (C) 2016 Wiley Periodicals, Inc.
Year
DOI
Venue
2017
10.1002/jgt.22051
JOURNAL OF GRAPH THEORY
Keywords
Field
DocType
plane graph,structural property,normal plane map,3-path
Normal plane,Combinatorics,Vertex (geometry),Structural property,Degree (graph theory),Mathematics,Planar graph,Bounded function
Journal
Volume
Issue
ISSN
85.0
1.0
0364-9024
Citations 
PageRank 
References 
2
0.39
9
Authors
3
Name
Order
Citations
PageRank
Oleg V. Borodin163967.41
Anna O. Ivanova217223.19
Alexandr V. Kostochka368289.87