TY - JOUR

T1 - A Degree Condition for the Existence of Regular Factors in K1, n-Free Graphs

AU - Ota, Katsuhiro

AU - Tokuda, Taro

PY - 1996/5

Y1 - 1996/5

N2 - A graph is called K1, n-free if it contains no K1, n as an induced subgraph. Let n(≥ 3), r be integers (if r is odd, r ≥ n - 1). We prove that every K1, n-free connected graph G with r|V(G)| even has an r-factor if its minimum degree is at least (n + n-1/r) ⌈n/2(n - 1) r⌉ - n - 1/r (⌈n/2(n - 1) r⌉)2 + n - 3. This degree condition is sharp.

AB - A graph is called K1, n-free if it contains no K1, n as an induced subgraph. Let n(≥ 3), r be integers (if r is odd, r ≥ n - 1). We prove that every K1, n-free connected graph G with r|V(G)| even has an r-factor if its minimum degree is at least (n + n-1/r) ⌈n/2(n - 1) r⌉ - n - 1/r (⌈n/2(n - 1) r⌉)2 + n - 3. This degree condition is sharp.

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U2 - 10.1002/(SICI)1097-0118(199605)22:1<59::AID-JGT8>3.0.CO;2-K

DO - 10.1002/(SICI)1097-0118(199605)22:1<59::AID-JGT8>3.0.CO;2-K

M3 - Article

AN - SCOPUS:0030551098

VL - 22

SP - 59

EP - 64

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -