Publikation: Zeitschriftenartikel

Rooted minors and locally spanning subgraphs

Grunddaten
Abstract
Autoren
Einrichtung

Grunddaten

Titel	Rooted minors and locally spanning subgraphs
Erscheinungsjahr	2024
Seiten (von – bis)	209 – 229
Band	105
Heft-Nr.	2
Jahr	2024
Publikationsform	Elektronische Ressource
Publikationsart	Zeitschriftenartikel
Sprache	Englisch
DOI	10.1002/jgt.23012
Letzte Änderung	13.03.2024 17:31:08
Bearbeitungsstatus	durch UB Rostock abschließend validiert
Dauerhafte URL	http://purl.uni-rostock.de/fodb/pub/71324
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Abstract

Results on the existence of various types of spanning subgraphs of graphs are milestones in structural graph theory and have been diversified in several directions. In the present paper, we consider "local" versions of such statements. In 1966, for instance, D. W. Barnette proved that a 3-connected planar graph contains a spanning tree of maximum degree at most 3. A local translation of this statement is that if G is a planar graph, X is a subset of specified vertices of G such that X cannot be separated in G by removing two or fewer vertices of G, then G has a tree of maximum degree at most 3 containing all vertices of X. Our results constitute a general machinery for strengthening statements about k-connected graphs (for 1 k 4) to locally spanning versions, that is, subgraphs containing a set X V (G) of a (not necessarily planar) graph G in which only X has high connectedness. Given a graph G and X V (G), we say M is a minor of G rooted at X, if M is a minor of G such that each bag of M contains at most one vertex of X and X is a subset of the union of all bags. We show that G has a highly connected minor rooted at X if X V (G) cannot be separated in G by removing a few vertices of G. Combining these investigations and the theory of Tutte paths in the planar case yields locally spanning versions of six well-known results about degree-bounded trees, Hamiltonian paths and cycles, and 2-connected subgraphs of graphs.

Autoren

Böhme, Thomas

Harant, Jochen

Kriesell, Matthias

Mohr, Samuel

Schmidt, Jens M.

Einrichtung

IEF/IN/IFI/Algorithmen und Komplexität