On the existence of a connected component of a graph

被引：6

作者：

Gura, Kirill ^{[1
]}

Hirst, Jeffry L. ^{[2
]}

Mummert, Carl ^{[1
]}

机构：

[1] Marshall Univ, Dept Math, 1 John Marshall Dr, Huntington, WV 25755 USA

[2] Appalachian State Univ, Dept Math Sci, Boone, NC 28608 USA

来源：

COMPUTABILITY-THE JOURNAL OF THE ASSOCIATION CIE | 2015年 / 4卷 / 02期

关键词：

Reverse mathematics; Weihrauch reducibility; component; graph; connected; partition; parallelization;

D O I：

10.3233/COM-150039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to ACA(0) over RCA(0). The problem of decomposing a countable graph into connected components is strongly Weihrauch equivalent to the problem of finding a single component, and each is equivalent to its infinite parallelization. For graphs with finitely many connected components, the existence of a connected component is either provable in RCA(0) or is equivalent to induction for Sigma(0)(2) formulas, depending on the formulation of the bound on the number of components.

引用

页码：103 / 117

页数：15

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