Abstract
We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)2/2 and (r + 1)2α(G) ⩽ 4rk(G), then G has an r‐factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r‐factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).
| Original language | English |
|---|---|
| Pages (from-to) | 63-69 |
| Number of pages | 7 |
| Journal | Journal of Graph Theory |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1989 Jan 1 |
| Externally published | Yes |
ASJC Scopus subject areas
- Geometry and Topology
Cite this
Independence number, connectivity, and r‐factors. / Nishimura, Tsuyoshi.
In: Journal of Graph Theory, Vol. 13, No. 1, 01.01.1989, p. 63-69.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Independence number, connectivity, and r‐factors
AU - Nishimura, Tsuyoshi
PY - 1989/1/1
Y1 - 1989/1/1
N2 - We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)2/2 and (r + 1)2α(G) ⩽ 4rk(G), then G has an r‐factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r‐factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).
AB - We show that if r ⩾ 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ⩾ (r + 1)2/2 and (r + 1)2α(G) ⩽ 4rk(G), then G has an r‐factor; if r ⩾ 2 is even and G is a graph with k(G) ⩾ r(r + 2)/2 and (r + 2)α(G) ⩽ 4k(G), then G has an r‐factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).
UR - http://www.scopus.com/inward/record.url?scp=84986468529&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84986468529&partnerID=8YFLogxK
U2 - 10.1002/jgt.3190130109
DO - 10.1002/jgt.3190130109
M3 - Article
AN - SCOPUS:84986468529
VL - 13
SP - 63
EP - 69
JO - Journal of Graph Theory
JF - Journal of Graph Theory
SN - 0364-9024
IS - 1
ER -