The Existence of Planar 4-Connected Essentially 6-Edge-Connected Graphs with No Claw-Decompositions
نویسندگان
چکیده
In 2006 Barát and Thomassen conjectured that every planar 4-edge-connected 4-regular simple graph of size divisible by three admits a claw-decomposition. Later, Lai (2007) disproved this conjecture family graphs with edge-connectivity 4 which the smallest one contains 24 vertices. note, we first give smaller counterexample having only 18 vertices next construct 4-connected essentially 6-edge-connected no claw-decompositions. This result provides sharpness for two known results say 5-edge-connected claw-decomposition if it is or planar.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2022
ISSN: ['1435-5914', '0911-0119']
DOI: https://doi.org/10.1007/s00373-022-02594-9