Abstract
An old conjecture by Jünger, Reinelt and Pulleyblank states that every 2-edge-connected planar graph can be decomposed into paths of length 3 and triangles, provided its size is divisible by 3. We prove the conjecture for a class of planar graphs including all 2-edge-connected series-parallel graphs. We also present a 2-edge-connected non-planar graph that can be embedded on the torus and admits no decomposition into paths of length 3 and triangles.
Original language | English |
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Journal | Electronic Notes in Discrete Mathematics |
Volume | 49 |
Issue number | November 2015 |
Pages (from-to) | 367-370 |
ISSN | 1571-0653 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- 3-path decomposition
- edge-decomposition
- planar graph
- 2-edge-connected
- series-parallel