Geodesic
Revising the Fellows-Kaschube $K_{3,3}$ Search
Journal of graph algorithms and applications, Tome 25 (2021) no. 1, pp. 513-520 Cet article a éte moissonné depuis la source Journal of Graph Algorythms and Applications website

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The first algorithm to achieve linear-time performance searching for and identifying a subgraph homeomorphic to $K_{3,3}$ is due to Fellows and Kaschube. Part of the proof of correctness depends on three cases of a straddling bridge of a subgraph homeomorphic to $K_5$ in an input graph. This paper presents a missing fourth case and revises the algorithm with an additional $K_{3,3}$ homeomorph isolator for the condition corresponding to the missing case. This paper also discusses why the prior proof of correctness missed the fourth case and presents a new proof of correctness showing that there are no other missing cases.
DOI : 10.7155/jgaa.00569
Keywords: subgraph homeomorphism, homeomorphic subgraph search, algorithm analysis 
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     title = {Revising the {Fellows-Kaschube} $K_{3,3}$ {Search}},
     journal = {Journal of graph algorithms and applications},
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     doi = {10.7155/jgaa.00569},
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John Boyer. Revising the Fellows-Kaschube $K_{3,3}$ Search. Journal of graph algorithms and applications, Tome 25 (2021) no. 1, pp. 513-520. doi: 10.7155/jgaa.00569

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