# On graphs G for which both g and G̅ are claw-free

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 3, page 267-272
- ISSN: 2083-5892

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topShinya Fujita. "On graphs G for which both g and G̅ are claw-free." Discussiones Mathematicae Graph Theory 25.3 (2005): 267-272. <http://eudml.org/doc/270325>.

@article{ShinyaFujita2005,

abstract = {Let G be a graph with |V(G)| ≥ 10. We prove that if both G and G̅ are claw-free, then minΔ(G), Δ(G̅) ≤ 2. As a generalization of this result in the case where |V(G)| is sufficiently large, we also prove that if both G and G̅ are $K_\{1,t\}$-free, then minΔ(G),Δ(G̅) ≤ r(t- 1,t)-1 where r(t-1,t) is the Ramsey number.},

author = {Shinya Fujita},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {claw-free; complement; maximum degree},

language = {eng},

number = {3},

pages = {267-272},

title = {On graphs G for which both g and G̅ are claw-free},

url = {http://eudml.org/doc/270325},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Shinya Fujita

TI - On graphs G for which both g and G̅ are claw-free

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 3

SP - 267

EP - 272

AB - Let G be a graph with |V(G)| ≥ 10. We prove that if both G and G̅ are claw-free, then minΔ(G), Δ(G̅) ≤ 2. As a generalization of this result in the case where |V(G)| is sufficiently large, we also prove that if both G and G̅ are $K_{1,t}$-free, then minΔ(G),Δ(G̅) ≤ r(t- 1,t)-1 where r(t-1,t) is the Ramsey number.

LA - eng

KW - claw-free; complement; maximum degree

UR - http://eudml.org/doc/270325

ER -

## References

top- [1] H.J. Broersma, Z. Ryjacek and I. Schiermeyer, Closure concepts - a survey, Graphs and Combin. 16 (2000) 17-48, doi: 10.1007/s003730050002.

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