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Displaying similar documents to “The number of spanning trees and chains of graphs.”

Spanning tree congestion of rook's graphs

Kyohei Kozawa, Yota Otachi (2011)

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.

Tree-Like Partial Hamming Graphs

Tanja Gologranc (2014)

Discussiones Mathematicae Graph Theory

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Tree-like partial cubes were introduced in [B. Brešar, W. Imrich, S. Klavžar, Tree-like isometric subgraphs of hypercubes, Discuss. Math. Graph Theory, 23 (2003), 227-240] as a generalization of median graphs. We present some incorrectnesses from that article. In particular we point to a gap in the proof of the theorem about the dismantlability of the cube graph of a tree-like partial cube and give a new proof of that result, which holds also for a bigger class of graphs, so called tree-like...