Abstract

We prove that every connected graph can be edge-decomposed into a spanning tree, an even graph, and a star forest.

Highlights

  • All graphs in this paper are simple and finite

  • We prove that every connected graph can be edge-decomposed into a spanning tree, an even graph, and a star forest

  • A decomposition of a graph G is a collection of edge-disjoint subgraphs whose union is G

Read more

Summary

Introduction

All graphs in this paper are simple and finite. A decomposition of a graph G is a collection of edge-disjoint subgraphs whose union is G. We prove that every connected graph can be edge-decomposed into a spanning tree, an even graph, and a star forest. The removal of the edges of a spanning tree results in a collection of cycles and paths. Every connected cubic graph can be decomposed into a spanning tree, a collection of cycles, and a matching.

Results
Conclusion

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 call

Disclaimer: 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.