#### Vol. 7, No. 2, 2014

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Spanning tree congestion of planar graphs

### Hiu Fai Law, Siu Lam Leung and Mikhail I. Ostrovskii

Vol. 7 (2014), No. 2, 205–226
##### Abstract

This paper is devoted to estimates of the spanning tree congestion for some planar graphs. We present three main results: (1) We almost determined (up to $±1$) the maximal possible spanning tree congestion for planar graphs. (2) The value of congestion indicator introduced by Ostrovskii [Discrete Math. 310, 1204–1209] can be very far from the value of the spanning tree congestion. (3) We find some more examples in which the congestion indicator can be used to find the exact value of the spanning tree congestion.

##### Keywords
dual graph, dual spanning tree, minimum congestion spanning tree, planar graph
##### Mathematical Subject Classification 2010
Primary: 05C05
Secondary: 05C10, 05C35