The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number W h(3,3)=9,W h(3,3,3)≥25 on a circle was calculated ...The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number W h(3,3)=9,W h(3,3,3)≥25 on a circle was calculated by computer.展开更多
Motivated by the connection with the genus of the corresponding link and its application on DNA polyhedral links,in this paper,we introduce a parameter s_(max)(G),which is the maximum number of circles of states of th...Motivated by the connection with the genus of the corresponding link and its application on DNA polyhedral links,in this paper,we introduce a parameter s_(max)(G),which is the maximum number of circles of states of the link diagram D(G)corresponding to a plane(positive)graph G.We show that s_(max)(G)does not depend on the embedding of G and if G is a 4-edge-connected plane graph then s_(max)(G)is equal to the number of faces of G,which cover the results of S.Y.Liu and H.P.Zhang as special cases.展开更多
文摘The big upper bound of typical van der Waerden number was investigated through calculating the van der Waerden number on a circle. And the van der Waerden number W h(3,3)=9,W h(3,3,3)≥25 on a circle was calculated by computer.
基金supported by the National Natural Science Foundation of China(Nos 11271307,11171279,11101174)。
文摘Motivated by the connection with the genus of the corresponding link and its application on DNA polyhedral links,in this paper,we introduce a parameter s_(max)(G),which is the maximum number of circles of states of the link diagram D(G)corresponding to a plane(positive)graph G.We show that s_(max)(G)does not depend on the embedding of G and if G is a 4-edge-connected plane graph then s_(max)(G)is equal to the number of faces of G,which cover the results of S.Y.Liu and H.P.Zhang as special cases.
