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Tank-Ring Factors in Supereulerian Claw-Free Graphs

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Abstract

A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of GC contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.

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Correspondence to He Jiang.

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Supported by Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) under grant No.: 200801410028 by Nature Science Foundation Project of Liaoning under Grant No.: 2201102038, and by Nature Science foundation of China (NSFC) under Grant No.: 61175062, 61100194.

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Li, M., Yuan, L., Jiang, H. et al. Tank-Ring Factors in Supereulerian Claw-Free Graphs. Graphs and Combinatorics 29, 599–608 (2013). https://doi.org/10.1007/s00373-011-1117-z

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  • DOI: https://doi.org/10.1007/s00373-011-1117-z

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