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On [formula omitted]-hamiltonicity of net-free line graphs
Faculty Author(s): Zhan, Mingquan
Student Author(s): -
Department: MATH
Publication: Discrete Mathematics
Year: 2021
Abstract: For integers s1,s2,s3>0, let Ns1,s2,s3 denote the graph obtained by identifying each vertex of a K3 with an end vertex of three disjoint paths Ps1+1, Ps2+1, Ps3+1 of length s1,s2 and s3, respectively. We prove the following results.(i) Let N1={Ns1,s2,s3:s1>0,s1≥s2≥s3≥0 and s1+s2+s3≤6}. Then for any N∈N1, every N-free line graph L(G) with |V(L(G))|≥s+3 is s-hamiltonian if and only if κ(L(G))≥s+2.(ii) Let N2={Ns1,s2,s3:s1>0,s1≥s2≥s3≥0 and s1+s2+s3≤4}. Then for any N∈N2, every N-free line graph L(G) with |V(L(G))|≥s+3 is s-Hamilton-connected if and only if κ(L(G))≥s+3.
Link: On [formula omitted]-hamiltonicity of net-free line graphs