For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph...For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph G is the minimum of k/d for which G admits a homomorphism to G^dk. The relationship between χc（ G- v） and χc （G）is investigated. In particular, the circular chromatic number of G^dk - v for any vertex v is determined. Some graphs withx χc（G - v） =χc（G） - 1 for any vertex v and with certain properties are presented. Some lower bounds for the circular chromatic number of a graph are studied, and a necessary and sufficient condition under which the circular chromatic number of a graph attains the lower bound χ- 1 ＋ 1/α is proved, where χ is the chromatic number of G and a is its independence number.展开更多
基金supported by Funding Project for Academic Human Resources Development in Institutionsof Higher Learning Under the Jurisdiction of Beijing Municipality(PHR(IHLB))National NaturalScience Fbundation of China under Grant No.10631070,No.60873205+2 种基金Beijing Natural Science Foundationunder Grant No.1092011Foundation of Beijing Education Commission under Grant No.SM200910037005Scientific Research Base foundation of Beijing Wuzi University.
基金The National Natural Science Foundation of China(No.10671033)
文摘For two integers k and d with （k, d） = 1 and k≥2d, let G^dk be the graph with vertex set {0,1,…k - 1 } in which ij is an edge if and only if d≤｜ i -j I｜≤k - d. The circular chromatic number χc（G） of a graph G is the minimum of k/d for which G admits a homomorphism to G^dk. The relationship between χc（ G- v） and χc （G）is investigated. In particular, the circular chromatic number of G^dk - v for any vertex v is determined. Some graphs withx χc（G - v） =χc（G） - 1 for any vertex v and with certain properties are presented. Some lower bounds for the circular chromatic number of a graph are studied, and a necessary and sufficient condition under which the circular chromatic number of a graph attains the lower bound χ- 1 ＋ 1/α is proved, where χ is the chromatic number of G and a is its independence number.
