CIRCULAR CHROMATIC NUMBER AND GRAPH MINORS

This paper proves that for any integer $n\geq 4$ and any rational number $r$, $2\leq r\leq n-2$, there exists a graph $G$ which has circular chromatic number $r$ and which does not contain $K_n$ as a minor.

[1]  Robin J. Wilson EVERY PLANAR MAP IS FOUR COLORABLE , 1991 .

[2]  David Moser,et al.  The star-chromatic number of planar graphs , 1997, J. Graph Theory.

[3]  David R. Guichard,et al.  Acyclic graph coloring and the complexity of the star chromatic number , 1993, J. Graph Theory.

[4]  Xuding Zhu,et al.  The circular chromatic number of series-parallel graphs of large odd girth , 2002, Discret. Math..

[5]  XUDING ZHU,et al.  Star chromatic numbers of graphs , 1996, Comb..

[6]  Robin Thomas,et al.  Hadwiger's conjecture forK6-free graphs , 1993, Comb..

[7]  Robin Thomas,et al.  The Four-Colour Theorem , 1997, J. Comb. Theory, Ser. B.

[8]  Xuding Zhu,et al.  Circular chromatic number: a survey , 2001, Discret. Math..

[9]  Xuding Zhu,et al.  Circular colouring and graph homomorphism , 1999, Bulletin of the Australian Mathematical Society.

[10]  Xuding Zhu,et al.  The circular chromatic number of series-parallel graphs with large girth , 2000 .

[11]  Xuding Zhu,et al.  The circular chromatic number of series-parallel graphs with large girth , 2000, J. Graph Theory.

[12]  A. Vince,et al.  Star chromatic number , 1988, J. Graph Theory.

[13]  Xuding Zhu Planar Graphs with Circular Chromatic Numbers between 3 and 4 , 1999, J. Comb. Theory, Ser. B.

[14]  Xuding Zhu A simple proof of Moser's theorem , 1999, J. Graph Theory.

[15]  Xuding Zhu,et al.  Uniquely H -colorable graphs with large girth , 1996 .

[16]  Pavol Hell,et al.  A note on the star chromatic number , 1990, J. Graph Theory.

[17]  Xuding Zhu Star chromatic numbers and products of graphs , 1992, J. Graph Theory.

[18]  Xuding Zhu Construction of uniquely H-colorable graphs , 1999, J. Graph Theory.