TY - JOUR
T1 - Induced Nets and Hamiltonicity of Claw-Free Graphs
AU - Chiba, Shuya
AU - Fujisawa, Jun
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Japan KK part of Springer Nature.
PY - 2021
Y1 - 2021
N2 - The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net, and the vertices of degree 1 in a net are called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced K1 , 3 is hamiltonian if every endvertex of each induced net of G has degree at least (| V(G) | - 2) / 3. In this paper we prove this conjecture in the affirmative.
AB - The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net, and the vertices of degree 1 in a net are called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced K1 , 3 is hamiltonian if every endvertex of each induced net of G has degree at least (| V(G) | - 2) / 3. In this paper we prove this conjecture in the affirmative.
KW - Claw-free graphs
KW - Hamiltonian cycles
KW - Induced nets
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U2 - 10.1007/s00373-020-02265-7
DO - 10.1007/s00373-020-02265-7
M3 - Article
AN - SCOPUS:85100971592
SN - 0911-0119
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
ER -