Abstract
The 3-decomposition conjecture is wide open. It asserts that every finite connected cubic graph can be decomposed into a spanning tree, a disjoint union of cycles, and a matching. We prove that the following graphs are reducible configurations for the 3-decomposition conjecture: the triangle, the K2,3, the claw-square, the twin-house, and the domino. As an application, we show that all 3-connected cubic graphs of path-width at most 4 satisfy the 3-decomposition conjecture.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
