Title of article :
Hamiltonicity of 3-connected line graphs
Author/Authors :
Yang، نويسنده , , Weihua and Xiong، نويسنده , , Liming and Lai، نويسنده , , Hongjian and Guo، نويسنده , , Xiaofeng، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2012
Pages :
4
From page :
1835
To page :
1838
Abstract :
Thomassen conjectured that every 4-connected line graph is Hamiltonian. Lai et al. conjectured [H. Lai, Y. Shao, H. Wu, J. Zhou, Every 3-connected, essentially 11-connected line graph is Hamiltonian, J. Combin. Theory Ser. B 96 (2006) 571–576] that every 3-connected, essentially 4-connected line graph is Hamiltonian. In this note, we first show that the conjecture posed by Lai et al. is not true and there is an infinite family of counterexamples; we show that 3-connected, essentially 4-connected line graph of a graph with at most 9 vertices of degree 3 is Hamiltonian; examples show that all conditions are sharp.
Keywords :
hamiltonian graph , Dominating Eulerian subgraph , Thomassen’s conjecture , Line graph , Super-Eulerian graphs , Collapsible graph
Journal title :
Applied Mathematics Letters
Serial Year :
2012
Journal title :
Applied Mathematics Letters
Record number :
1528553
Link To Document :
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