# Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

Discussiones Mathematicae Graph Theory (1996)

- Volume: 16, Issue: 2, page 173-179
- ISSN: 2083-5892

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topSebastian Urbański. "Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅." Discussiones Mathematicae Graph Theory 16.2 (1996): 173-179. <http://eudml.org/doc/270305>.

@article{SebastianUrbański1996,

abstract = {The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.},

author = {Sebastian Urbański},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Folkman numbers; Kₙ-free graphs; extremal graph theory; generalized Ramsey theory; extremal graph; monochromatic triangle; Ramsey property; vertex coloring},

language = {eng},

number = {2},

pages = {173-179},

title = {Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅},

url = {http://eudml.org/doc/270305},

volume = {16},

year = {1996},

}

TY - JOUR

AU - Sebastian Urbański

TI - Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

JO - Discussiones Mathematicae Graph Theory

PY - 1996

VL - 16

IS - 2

SP - 173

EP - 179

AB - The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.

LA - eng

KW - Folkman numbers; Kₙ-free graphs; extremal graph theory; generalized Ramsey theory; extremal graph; monochromatic triangle; Ramsey property; vertex coloring

UR - http://eudml.org/doc/270305

ER -

## References

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- [11] R.W. Irving, On a bound of Graham and Spencer for graph-coloring constant, J. Combin. Theory 15 (1973) 200-203, doi: 10.1016/0095-8956(73)90021-X. Zbl0247.05119
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