Forest decompositions of graphs with cyclomatic number 3.
Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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Norbert Polat (1991)
Czechoslovak Mathematical Journal
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Farrell, E.J. (1983)
International Journal of Mathematics and Mathematical Sciences
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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...
Norbert Polat (2001)
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.
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.