Abstract
The scattering number of a graph G equals max { c( G⧹ S) − | S| S is a cutset of G} where c( G⧹ S) denotes the number of connected components in G⧹ S. Jung (1978) has given for any graph having no induced path on four vertices ( P 4-free graph) a correspondence between the value of its scattering number and the existence of Hamiltonian paths or Hamiltonian cycles. Hochstättler and Tinhofer (to appear) studied the Hamiltonicity of P 4-sparse graphs introduced by Hoàng (1985). In this paper, using modular decomposition, we show that the results of Jung and Hochsta̋ttler and Tinhofer can be generalized to a subclass of the family of semi- P 4-sparse graphs introduced in Fouquet and Giakoumakis (to appear).
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