## Displaying similar documents to “Spanning trees of infinite graphs”

### End-faithful spanning trees of countable graphs with prescribed sets of rays

Czechoslovak Mathematical Journal

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We prove that a countable connected graph has an end-faithful spanning tree that contains a prescribed set of rays whenever this set is countable, and we show that this solution is, in a certain sense, the best possible. This improves a result of Hahn and Širáň Theorem 1.

### Spanning tree congestion of rook's graphs

Discussiones Mathematicae Graph Theory

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Let G be a connected graph and T be a spanning tree of G. For e ∈ E(T), the congestion of e is the number of edges in G joining the two components of T - e. The congestion of T is the maximum congestion over all edges in T. The spanning tree congestion of G is the minimum congestion over all its spanning trees. In this paper, we determine the spanning tree congestion of the rook's graph Kₘ ☐ Kₙ for any m and n.

### Independence number and degree bounded spanning tree.

Applied Mathematics E-Notes [electronic only]

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### Spanning trees with leaves bounded by independence number.

Applied Mathematics E-Notes [electronic only]

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### Multi-faithful spanning trees of infinite graphs

Czechoslovak Mathematical Journal

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For an end $\tau$ and a tree $T$ of a graph $G$ we denote respectively by $m\left(\tau \right)$ and ${m}_{T}\left(\tau \right)$ the maximum numbers of pairwise disjoint rays of $G$ and $T$ belonging to $\tau$, and we define $\mathrm{t}m\left(\tau \right):=min\left\{{m}_{T}\left(\tau \right)\phantom{\rule{0.222222em}{0ex}}T\text{is}\text{a}\text{spanning}\text{tree}\text{of}G\right\}$. 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 $f\left(\tau \right)$ such that $\mathrm{t}m\left(\tau \right)\le f\left(\tau \right)\le m\left(\tau \right)$, there exists a spanning tree $T$ of $G$ such that ${m}_{T}\left(\tau \right)=f\left(\tau \right)$ for every end $\tau$ of $G$.

### On reconstructing of infinite forests

Commentationes Mathematicae Universitatis Carolinae

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### On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k

Discussiones Mathematicae Graph Theory

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A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σk(G) ≥ |V (G)|+s−1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree less than...