Matching Numbers and Dimension of Edge Ideals

Hirano, Ayana; Matsuda, Kazunori

doi:10.1007/s00373-021-02277-x

Cited by 2 publications

(1 citation statement)

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“…Thus, many scholars are committed to the research of induced matching problem. In particular, there have been many important achievements in the study on induced matching number, for example, Romeo, Hibi, Panda et al ([4-6]) calculated the induced matching number of some special graphs; Ajayi et al( [7]) determined the some bounds on the maximum induced matching numbers of certain grids; Hirano et al ( [8]) studied the relationship between matching number, induced matching number and dimension of edge ideals of graph. Recently, counting problem on the total number of induced matchings was introduced by Liu et al (2021) ( [9]).…”

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confidence: 99%

Counting the Total Induced Matchings for Recursive Trees

2022

Proceedings of 2022 the 12th International Workshop on Computer Science and Engineering

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An induced matching of the graph G is a matching which forms an induced subgraph of 1regular in G. Induced matching is widely used in computer networks, such as communication network testing, concurrent transmission of messages, secure communication channels etc. Counting problem on the total number of induced matchings was introduced by Liu et al. (2021). In view of its computational difficulty, the total number of induced matchings for restricted graph is therefore of interest. By combination method and characteristic equation we get the closed formulas of the total number of induced matchings for some recursive trees.

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confidence: 99%