The degree-diameter problem for sparse graph classes

被引：0
|
作者：
Pineda-Villavicencio, Guillermo [1 ]
Wood, David R. [2 ]
机构：
[1] Federat Univ Australia, Ctr Informat & Appl Optimisat, Ballarat, Vic, Australia
[2] Monash Univ, Sch Math Sci, Melbourne, Vic 3004, Australia
来源：
ELECTRONIC JOURNAL OF COMBINATORICS | 2015年 / 22卷 / 02期
基金：
澳大利亚研究理事会;
关键词：
degree-diameter problem; treewidth; arboricity; sparse graph; surface graph; apex-minor-free graph; EXTREMAL FUNCTION; PLANAR GRAPHS;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The degree-diameter problem asks for the maximum number of vertices in a graph with maximum degree Delta and diameter k. For fixed k, the answer is Theta(Delta(k)). We consider the degree-diameter problem for particular classes of sparse graphs, and establish the following results. For graphs of bounded average degree the answer is Theta(Delta(k-1)), and for graphs of bounded arboricity the answer is Theta(Delta([k/2])) in both cases for fixed k. For graphs of given treewidth, we determine the the maximum number of vertices up to a constant factor. Other precise bounds are given for graphs embeddable on a given surface and apex-minor-free graphs.
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页数：20
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