Abstract
A vertex set in a graph is a connected set if it induces a connected subgraph. For a tree T, each subgraph induced by a connected set of T is actually a subtree of T. The number and average size of subtrees of a tree T are two well-studied parameters. Yan and Yeh developed a linear-time algorithm for computing the number of subtrees in a tree through “generating function”. In this paper, we present linear-time algorithms for computing the number and average size of connected sets in a planar 3-tree.
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The authors would like to thank anonymous referees for their careful reading and valuable suggestions, which have improved the presentation of this paper.
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This work was supported by National Natural Science Foundation of China (No. 12271251).
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Luo, Z., Xu, K. Computing the Number and Average Size of Connected Sets in Planar 3-Trees. Graphs and Combinatorics 40, 55 (2024). https://doi.org/10.1007/s00373-024-02783-8
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DOI: https://doi.org/10.1007/s00373-024-02783-8