Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems
β Scribed by Zhang, Heping; Lam, Peter Che Bor; Shiu, Wai Chee
- Book ID
- 118197698
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2008
- Tongue
- English
- Weight
- 414 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0895-4801
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## Abstract We give examples of edgeβchromatic critical graphs __G__ of the following types: (i) of even order and having no 1βfactor, and (ii) of odd order and having a vertex __v__ of minimum degree such that __G__ β __v__ has no 1βfactor. The first disproves a conjecture of S. Fiorini and R. J.
A graph is called K1,.-free if it contains no K l , n as an induced subgraph. Let n ( r 3), r be integers (if r is odd, r 2 n -1). We prove that every Kl,,-free connected graph G with rlV(G)I even has an r-factor if its minimum degree is at least This degree condition is sharp.