Multi-faithful spanning trees of infinite graphs

Title:

Multi-faithful spanning trees of infinite graphs

Creator:

Polat, Norbert

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:70732122-621e-482a-ba13-6256735a3170
uuid:70732122-621e-482a-ba13-6256735a3170

Subject:

infinite graph, end, end-faithful, spanning tree, and multiplicity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

For an end $\tau $ and a tree $T$ of a graph $G$ we denote respectively by $m(\tau )$ and $m_{T}(\tau )$ the maximum numbers of pairwise disjoint rays of $G$ and $T$ belonging to $\tau $, and we define $\mathop {\mathrm tm}(\tau ) := \min \lbrace m_{T}(\tau )\: T \text{is} \text{a} \text{spanning} \text{tree} \text{of} G \rbrace $. In this paper we give partial answers—affirmative and negative ones—to the general problem of determining if, for a function $f$ mapping every end $\tau $ of $G$ to a cardinal $f(\tau )$ such that $\mathop {\mathrm tm}(\tau ) \le f(\tau ) \le m(\tau )$, there exists a spanning tree $T$ of $G$ such that $m_{T}(\tau ) = f(\tau )$ for every end $\tau $ of $G$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

477-492

Source:

Czechoslovak Mathematical Journal | 2001 Volume:51 | Number:3

Harvested from:

CDK

Metadata only:

false