# On the cost chromatic number of outerplanar, planar, and line graphs

John Mitchem; Patrick Morriss; Edward Schmeichel

Discussiones Mathematicae Graph Theory (1997)

- Volume: 17, Issue: 2, page 229-241
- ISSN: 2083-5892

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topJohn Mitchem, Patrick Morriss, and Edward Schmeichel. "On the cost chromatic number of outerplanar, planar, and line graphs." Discussiones Mathematicae Graph Theory 17.2 (1997): 229-241. <http://eudml.org/doc/270344>.

@article{JohnMitchem1997,

abstract = {We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and construct several infinite classes of counterexamples to a conjecture of Harary and Plantholt on the cost chromatic number of line graphs.},

author = {John Mitchem, Patrick Morriss, Edward Schmeichel},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {cost coloring; outerplanar; planar; line graphs; maximal outerplanar and maximal planar graphs},

language = {eng},

number = {2},

pages = {229-241},

title = {On the cost chromatic number of outerplanar, planar, and line graphs},

url = {http://eudml.org/doc/270344},

volume = {17},

year = {1997},

}

TY - JOUR

AU - John Mitchem

AU - Patrick Morriss

AU - Edward Schmeichel

TI - On the cost chromatic number of outerplanar, planar, and line graphs

JO - Discussiones Mathematicae Graph Theory

PY - 1997

VL - 17

IS - 2

SP - 229

EP - 241

AB - We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost chromatic number of maximal outerplanar and maximal planar graphs can be arbitrarily large and construct several infinite classes of counterexamples to a conjecture of Harary and Plantholt on the cost chromatic number of line graphs.

LA - eng

KW - cost coloring; outerplanar; planar; line graphs; maximal outerplanar and maximal planar graphs

UR - http://eudml.org/doc/270344

ER -

## References

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