On the smallest snarks with oddness 4 and connectivity 2
نویسنده
چکیده
A snark is a bridgeless cubic graph which is not 3-edge-colourable. The oddness of a bridgeless cubic graph is the minimum number of odd components in any 2factor of the graph. Lukot’ka, Mácajová, Mazák and Škoviera showed in [Electron. J. Combin. 22 (2015)] that the smallest snark with oddness 4 has 28 vertices and remarked and that there are exactly two such graphs of that order. However, this remark is incorrect as – using an exhaustive computer search – we show that there are in fact three snarks with oddness 4 on 28 vertices. In this note we present the missing snark and also determine all snarks with oddness 4 up to 34 vertices.
منابع مشابه
Smallest snarks with oddness 4 and cyclic connectivity 4 have order 44
The family of snarks – connected bridgeless cubic graphs that cannot be 3edge-coloured – is well-known as a potential source of counterexamples to several important and long-standing conjectures in graph theory. These include the cycle double cover conjecture, Tutte’s 5-flow conjecture, Fulkerson’s conjecture, and several others. One way of approaching these conjectures is through the study of ...
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عنوان ژورنال:
- CoRR
دوره abs/1710.00757 شماره
صفحات -
تاریخ انتشار 2017