Length-constrained path-matchings in graphs
✍ Scribed by M. Ghodsi; M. T. Hajiaghayi; M. Mahdian; V. S. Mirrokni
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 114 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0028-3045
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We generalize Kasteleyn's method of enumerating the perfect matchings in a planar graph to graphs embedding on an arbitrary compact boundaryless 2-manifold S. Kasteleyn stated that perfect matchings in a graph embedding on a surface of genus g could be enumerated as a linear combination of 4 g Pfaff
## Abstract For a graph __G__, let __p(G)__ denote the order of a longest path in __G__ and __c(G)__ the order of a longest cycle in __G__, respectively. We show that if __G__ is a 3‐connected graph of order __n__ such that $\textstyle{\sum^{4}\_{i=1}\,{\rm deg}\_{G}\,x\_{i} \ge {3\over2}\,n + 1}$
## Abstract We prove that a 171‐edge‐connected graph has an edge‐decomposition into paths of length 3 if and only its size is divisible by 3. It is a long‐standing problem whether 2‐edge‐connectedness is sufficient for planar triangle‐free graphs, and whether 3‐edge‐connectedness suffices for graph