Hamilton Paths in Dominating Graphs of Trees and Cycles

被引：1

作者：

Adaricheva, Kira ^{[1
]}

Blake, Heather Smith ^{[2
]}

Bozeman, Chassidy ^{[3
]}

Clarke, Nancy E. ^{[4
]}

Haas, Ruth ^{[5
]}

Messinger, Margaret-Ellen ^{[6
]}

Seyffarth, Karen ^{[7
]}

机构：

[1] Hofstra Univ, Dept Math, Hempstead, NY 11549 USA

[2] Davidson Coll, Dept Math & Comp Sci, Davidson, NC 28035 USA

[3] Mt Holyoke Coll, Dept Math & Stat, S Hadley, MA 01075 USA

[4] Acadia Univ, Dept Math & Stat, Wolfville, NS B4P 2R6, Canada

[5] Univ Hawaii Manoa, Dept Math, Honolulu, HI 96822 USA

[6] Mt Allison Univ, Dept Math & Comp Sci, Sackville, NB E4L 1E2, Canada

[7] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

来源：

GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 06期

基金：

美国国家科学基金会;

关键词：

Reconfiguration; Domination; Hamilton paths;

D O I：

10.1007/s00373-022-02579-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The dominating graph of a graph H has as its vertices all dominating sets of H, with an edge between two dominating sets if one can be obtained from the other by the addition or deletion of a single vertex of H. In this paper we prove that the dominating graph of any tree has a Hamilton path. We also show how a result about binary strings leads to a proof that the dominating graph of a cycle on n vertices has a Hamilton path if and only if n is not a multiple of 4.

引用

页数：9

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