# On path-quasar Ramsey numbers

Annales UMCS, Mathematica (2015)

- Volume: 68, Issue: 2, page 11-17
- ISSN: 2083-7402

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topBinlong Li, and Bo Ning. "On path-quasar Ramsey numbers." Annales UMCS, Mathematica 68.2 (2015): 11-17. <http://eudml.org/doc/270004>.

@article{BinlongLi2015,

abstract = {Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or Ḡ contains a G2. Parsons gave a recursive formula to determine the values of R(Pn,K1,m), where Pn is a path on n vertices and K1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn,K1,m), where Pn is a linear forest on m vertices. We determine the exact values of R(Pn,K1∨Fm) for the cases m ≤ n and m ≥ 2n, and for the case that Fm has no odd component. Moreover, we give a lower bound and an upper bound for the case n+1 ≤ m ≤ 2n−1 and Fm has at least one odd component.},

author = {Binlong Li, Bo Ning},

journal = {Annales UMCS, Mathematica},

keywords = {Ramsey number; path; star; quasar},

language = {eng},

number = {2},

pages = {11-17},

title = {On path-quasar Ramsey numbers},

url = {http://eudml.org/doc/270004},

volume = {68},

year = {2015},

}

TY - JOUR

AU - Binlong Li

AU - Bo Ning

TI - On path-quasar Ramsey numbers

JO - Annales UMCS, Mathematica

PY - 2015

VL - 68

IS - 2

SP - 11

EP - 17

AB - Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or Ḡ contains a G2. Parsons gave a recursive formula to determine the values of R(Pn,K1,m), where Pn is a path on n vertices and K1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn,K1,m), where Pn is a linear forest on m vertices. We determine the exact values of R(Pn,K1∨Fm) for the cases m ≤ n and m ≥ 2n, and for the case that Fm has no odd component. Moreover, we give a lower bound and an upper bound for the case n+1 ≤ m ≤ 2n−1 and Fm has at least one odd component.

LA - eng

KW - Ramsey number; path; star; quasar

UR - http://eudml.org/doc/270004

ER -

## References

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- [7] Parsons, T. D., Path-star Ramsey numbers, J. Combin. Theory, Ser. B 17 (1) (1974), 51-58. Zbl0282.05110
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- [9] Salman, A. N. M., Broersma, H. J., Path-fan Ramsey numbers, Discrete Applied Math. 154 (9) (2006), 1429-1436. Zbl1093.05043
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- [11] Zhang, Y., On Ramsey numbers of short paths versus large wheels, Ars Combin. 89 (2008), 11-20. Zbl1224.05346

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