TY - JOUR
T1 - Construction of K n-minor free graphs with given circular chromatic number
AU - Liaw, Sheng Chyang
AU - Pan, Zhishi
AU - Zhu, Xuding
PY - 2003/2/28
Y1 - 2003/2/28
N2 - For each integer n5 and each rational number r in the interval [2,n-1], we construct a K n-minor free graph G with χ c(G)=r. This answers a question asked by Zhu (Discrete Mathematics, 229 (1-3) (2001) 371). In case n=5, the constructed graphs are actually planar. Such planar graphs were first constructed in J. Graph Theory 24 (1997) 33 (for ∈[2,3]) and in J. Combin. Theory 76 (1999) 170 (for r∈[3,4]). However, our construction and proof are much simpler.
AB - For each integer n5 and each rational number r in the interval [2,n-1], we construct a K n-minor free graph G with χ c(G)=r. This answers a question asked by Zhu (Discrete Mathematics, 229 (1-3) (2001) 371). In case n=5, the constructed graphs are actually planar. Such planar graphs were first constructed in J. Graph Theory 24 (1997) 33 (for ∈[2,3]) and in J. Combin. Theory 76 (1999) 170 (for r∈[3,4]). However, our construction and proof are much simpler.
KW - Circular chromatic number
KW - Hadwiger conjecture
KW - K -minor free graphs
KW - Planar graphs
KW - Series-parallel construction
UR - http://www.scopus.com/inward/record.url?scp=84867974761&partnerID=8YFLogxK
U2 - 10.1016/S0012-365X(02)00529-0
DO - 10.1016/S0012-365X(02)00529-0
M3 - 期刊論文
AN - SCOPUS:84867974761
SN - 0012-365X
VL - 263
SP - 191
EP - 206
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -