A note on independent sets in trees
Summary (1 min read)
Summary
- The authors also characterize those trees achieving this maximum value.
- Finally the authors investigate some related problems.
- Key words, independent vertices, trees, extremal graphs AMS(MOS) subject classifications.
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Citations
14 citations
Cites background from "A note on independent sets in trees..."
...Sagan [24] gave a graph-theoretical demonstration of Wilf’s bound....
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13 citations
Cites background from "A note on independent sets in trees..."
...Proposed running head: Maximal Independent Sets And Cycles Send proofs to: Bruce E. Sagan Department of Mathematics Michigan State University East Lansing, MI 48824-1027 Tel....
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...For trees, Wilf (in the paper cited previously) determined the maximum, while Sagan [8] also found the graphs achieving this value....
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12 citations
Cites background from "A note on independent sets in trees..."
...The same holds, of course, for the number of independent sets....
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12 citations
12 citations
Cites background from "A note on independent sets in trees..."
...On the other hand, Hujter and Tuza [4] give credit to Poljak [9] for his presenting the tree S(K1,d ), the subdivision of the star with d rays (d 1), which is the only VI-extremal tree of odd order 2d + 1 which appears in Wilf’s paper and Sagan’s characterization....
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...Moreover, they correct Sagan’s quotation of the unpublished characterization (due to Griggs and Grinstead) of n-vertex VI-extremal forests....
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...Those “some” graphs are: any graphs (with cliques in place of independent sets)—Moon and Moser [8]; trees—Wilf [17], Sagan [10], and Zito [18]; connected graphs—Füredi [2], Griggs, et al. [3]; bipartite—Liu [19]; triangle-free—Hujter and Tuza [4]....
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...Those “some” graphs are: any graphs (with cliques in place of independent sets)—Moon and Moser [8]; trees—Wilf [17], Sagan [10], and Zito [18]; connected graphs—Füredi [2], Griggs, et al....
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References
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