The Hamiltonian properties in K1,r-free split graphs

For a connected graph F of order at least three, we say that a graph G is F-free if G does not contain an induced subgraph isomorphic to F. We call a connected graph G a split graph if the vertex set of G can be partitioned into a clique and an independent set. Motivated by a hamiltonicity result due to Renjith and Sadagopan (arXiv:1610 .00855v3), involving K-1,K-3-free split graphs, we study the hamiltonian properties of K-1,K-r-free split graphs. In our first main result, we show that a K-1,K-3-free split graph G is pancyclic if and only if G is 2-connected, which improves a result of Renjith and Sadagopan. Also, we prove that a K-1,K-4-free split graph G is hamiltonian if G is 3-connected. Further, we give a conjecture as following: Let G be a K-1,K-r+1-free split graph with at least three vertices. If G is r-connected, then G is hamiltonian. (C)& nbsp;2022 Elsevier B.V. All rights reserved.