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- W2553677891 abstract "The classes of odd graphs $O_n$ and middle levels graphs $B_n$ form one parameter subclasses of the Kneser graphs and bipartite Kneser graphs respectively. In particular both classes are vertex transitive while resisting definitive conclusions about their Hamiltonicity, and have thus come under scrutiny with regards to the Lovasz conjecture. In this paper, we will establish that middle levels graphs may always be embedded in odd graphs and middle levels graphs of higher degree, and furthermore, that this embedding allows us to define a recursion relationship in both classes which can be used to lift paths in $O_{n-1}$ (respectively $B_{n-1}$) to paths in $O_n$ (respectively $B_n$). This embedding also gives rise to the natural formation of a class of biregular graphs which give connections between the odd graphs, middle levels graphs and Catalan numbers." @default.
- W2553677891 created "2016-11-30" @default.
- W2553677891 creator A5005620245 @default.
- W2553677891 date "2016-11-19" @default.
- W2553677891 modified "2023-09-26" @default.
- W2553677891 title "Recursive Relationships in the Classes of Odd Graphs and Middle Levels Graphs" @default.
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- W2553677891 hasPublicationYear "2016" @default.
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