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Balanced generic circuits without long paths
2012
Discrete Mathematics
We call a graph G = (V , E) a (k, ℓ)-circuit if |E| = k|V | − ℓ + 1 and every X ⊂ V with 2 ≤ |X| ≤ |V | − 1 induces at most k|X | − ℓ edges. A (2, 3)-circuit is also called a generic circuit. We say that a graph is balanced if the difference between its maximum and minimum degrees is at most 1. Graver et al. asked in Graver et al. (1993) [7] whether a balanced generic circuit always admits a decomposition into two disjoint Hamiltonian paths. We show that this does not hold, moreover there are
doi:10.1016/j.disc.2012.03.031
fatcat:ylplleudtnen5ckbtujhpliasu