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Full-Text Articles in Physical Sciences and Mathematics
Degree And Neighborhood Conditions For Hamiltonicity Of Claw-Free Graphs, Zhi-Hong Chen
Degree And Neighborhood Conditions For Hamiltonicity Of Claw-Free Graphs, Zhi-Hong Chen
Scholarship and Professional Work - LAS
For a graph H , let σ t ( H ) = min { Σ i = 1 t d H ( v i ) | { v 1 , v 2 , … , v t } is an independent set in H } and let U t ( H ) = min { | ⋃ i = 1 t N H ( v i ) | | { v 1 , v 2 , ⋯ , v t } is an independent set in H } . We show that for a given number ϵ and given integers …
Circumferences Of 3-Connected Claw-Free Graphs, Ii, Zhi-Hong Chen
Circumferences Of 3-Connected Claw-Free Graphs, Ii, Zhi-Hong Chen
Scholarship and Professional Work - LAS
For a graph H , the circumference of H , denoted by c ( H ) , is the length of a longest cycle in H . It is proved in Chen (2016) that if H is a 3-connected claw-free graph of order n with δ ≥ 8 , then c ( H ) ≥ min { 9 δ − 3 , n } . In Li (2006), Li conjectured that every 3-connected k -regular claw-free graph H of order n has c ( H ) ≥ min { 10 k − 4 , n } . Later, Li posed …