Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: There are many long-standing open problems on cubic bridgeless graphs, for instance, Jaeger’s directed cycle double cover conjecture. On the other hand, many structural properties of braces have been recently discovered. In this work,  bijectively map the cubic bridgeless graphs to braces which  call the hexagon graphs, and explore the structure of hexagon graphs.  show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig’s augmentations. In addition,  present a reformulation of Jaeger’s directed cycle double cover conjecture in the class of hexagon graphs.
['Andrea Jiménez', 'Mihyun Kang', 'Martin Loebl']
I am writing a research paper on a idea Cubic Bridgeless Graphs and Braces
[{"from": "human", "value": "I am writing a research paper on a idea Cubic Bridgeless Graphs and Braces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: There are many long-standing open problems on cubic bridgeless graphs, for instance, Jaeger\u2019s directed cycle double cover conjecture. On the other hand, many structural properties of braces have been recently discovered. In this work,  bijectively map the cubic bridgeless graphs to braces which  call the hexagon graphs, and explore the structure of hexagon graphs.  show that hexagon graphs are braces that can be generated from the ladder on 8 vertices using two types of McCuaig\u2019s augmentations. In addition,  present a reformulation of Jaeger\u2019s directed cycle double cover conjecture in the class of hexagon graphs."}]