For trees the lion number satisfies pw(T) ≤ L(T) ≤ pw(T)+1; for connected graphs L(G) ≤ pw(G)+1 and the monotone lion number obeys pw(G) ≤ L^m(G) ≤ 2pw(G)+2, with monotonicity holding for isometric subgraphs but not arbitrary ones.
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Lions and Contamination: Trees and General Graphs
For trees the lion number satisfies pw(T) ≤ L(T) ≤ pw(T)+1; for connected graphs L(G) ≤ pw(G)+1 and the monotone lion number obeys pw(G) ≤ L^m(G) ≤ 2pw(G)+2, with monotonicity holding for isometric subgraphs but not arbitrary ones.