A Note on Observables for Counting Trails and Paths in Graphs
β Scribed by Fotini Markopoulou; Simone Severini
- Publisher
- Springer Netherlands
- Year
- 2009
- Tongue
- English
- Weight
- 265 KB
- Volume
- 8
- Category
- Article
- ISSN
- 1570-1166
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π SIMILAR VOLUMES
## Abstract In the study of decompositions of graphs into paths and cycles, the following questions have arisen: Is it true that every graph __G__ has a smallest path (resp. pathβcycle) decomposition __P__ such that every odd vertex of __G__ is the endpoint of exactly one path of __P__? This note g
C. Thomassen extended Tutte's theorem on cycles in planar graphs in the paper "A Theorem on Paths in Planar Graphs". This note corrects a flaw in his proof.
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The problem of finding A-trails in plane Eulerian graphs is &'P-complete even for 3-connected graphs, as shown by the first two authors in an earlier paper. In the present paper, we discuss sufficient conditions for the existence of an A-trail in a 2-connected plane Eulerian graph. They generalize t