Displaying similar documents to “On the size of a maximal induced tree in a random graph”

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.

A lower bound for the irredundance number of trees

Michael Poschen, Lutz Volkmann (2006)

Discussiones Mathematicae Graph Theory

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Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leaves of a graph G are denoted by n(G) and n₁(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T) ≥ (n(T) + 2 - n₁(T))/3. In this paper we prove ir(T) ≥ (n(T) + 2 - n₁(T))/3. for an arbitrary tree T. Since γ(T) ≥ ir(T) is always valid, this inequality is an extension and improvement of...