Edge Disjoint Hamilton Cycles in Knödel Graphs

Palanivel Subramania Nadar Paulraja (1) , S Sampath Kumar (2)

1 Department of Mathematics, Kalasalingam University
2 Department of Mathematics, SSN College of Engineering

The vertices of the Knödel graph $W_{\Delta, n}$ on $n \geq 2$ vertices, $n$ even, and of maximum degree $\Delta, 1 \leq \Delta \leq \lfloor log_2(n) \rfloor$, are the pairs $(i,j)$ with $i=1,2$ and $0 \leq j \leq \frac{n}{2} -1$. For $0 \leq j \leq \frac{n}{2} -1$, there is an edge between vertex $(1,j)$ and every vertex $(2,j + 2^k - 1 (mod \frac{n}{2}))$, for $k=0,1,2, \ldots , \Delta -1$. Existence of a Hamilton cycle decomposition of $W_{k, 2k}, k \geq 6$ is not yet known, see Discrete Appl. Math. 137 (2004) 173-195. In this paper, it is shown that the $k$-regular Knödel graph $W_{k,2k}, k \geq 6$ has $ \lfloor \frac{k}{2} \rfloor - 1$ edge disjoint Hamilton cycles.

Mots clés: Knödel Graphs; Hamilton Cycle Decomposition; Tensor Product; Bieulerian Graph

Domaines: Mathématique discrète [cs.DM]

Palanivel Subramania Nadar Paulraja, S Sampath Kumar. Edge Disjoint Hamilton Cycles in Knödel Graphs. Discrete Mathematics and Theoretical Computer Science, 2016, Vol. 17 no. 3 (3), pp.263-284. ⟨10.46298/dmtcs.2148⟩. ⟨hal-01352842⟩