# The Mycielskian of a Graph

Formalized Mathematics (2011)

- Volume: 19, Issue: 1, page 27-34
- ISSN: 1426-2630

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topPiotr Rudnicki, and Lorna Stewart. "The Mycielskian of a Graph." Formalized Mathematics 19.1 (2011): 27-34. <http://eudml.org/doc/267007>.

@article{PiotrRudnicki2011,

abstract = {Let ω(G) and χ(G) be the clique number and the chromatic number of a graph G. Mycielski [11] presented a construction that for any n creates a graph Mn which is triangle-free (ω(G) = 2) with χ(G) > n. The starting point is the complete graph of two vertices (K2). M(n+1) is obtained from Mn through the operation μ(G) called the Mycielskian of a graph G.We first define the operation μ(G) and then show that ω(μ(G)) = ω(G) and χ(μ(G)) = χ(G) + 1. This is done for arbitrary graph G, see also [10]. Then we define the sequence of graphs Mn each of exponential size in n and give their clique and chromatic numbers.},

author = {Piotr Rudnicki, Lorna Stewart},

journal = {Formalized Mathematics},

keywords = {clique number; chromatic number; Mycielskian},

language = {eng},

number = {1},

pages = {27-34},

title = {The Mycielskian of a Graph},

url = {http://eudml.org/doc/267007},

volume = {19},

year = {2011},

}

TY - JOUR

AU - Piotr Rudnicki

AU - Lorna Stewart

TI - The Mycielskian of a Graph

JO - Formalized Mathematics

PY - 2011

VL - 19

IS - 1

SP - 27

EP - 34

AB - Let ω(G) and χ(G) be the clique number and the chromatic number of a graph G. Mycielski [11] presented a construction that for any n creates a graph Mn which is triangle-free (ω(G) = 2) with χ(G) > n. The starting point is the complete graph of two vertices (K2). M(n+1) is obtained from Mn through the operation μ(G) called the Mycielskian of a graph G.We first define the operation μ(G) and then show that ω(μ(G)) = ω(G) and χ(μ(G)) = χ(G) + 1. This is done for arbitrary graph G, see also [10]. Then we define the sequence of graphs Mn each of exponential size in n and give their clique and chromatic numbers.

LA - eng

KW - clique number; chromatic number; Mycielskian

UR - http://eudml.org/doc/267007

ER -

## References

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