Abstract
The well-known 1–2–3 Conjecture asserts that the edges of every graph without an isolated edge can be weighted with 1, 2 and 3 so that adjacent vertices receive distinct weighted degrees. This is open in general. The Standard (2,2)-Conjecture asserts that every graph with no isolated edge and no isolated triangle can be decomposed into two graphs, each of which can be weighted with 1, 2 for the same goal. We prove that this conjecture holds for graphs with minimum degree δ≥106. The proof is in particular based on applications of the Lovász Local Lemma and theorems on degree-constrained subgraphs.
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.
