{"title":"Acyclic improper colourings of graphs with bounded degree","authors":"P. Boiron, É. Sopena, L. Vignal","doi":"10.1090/dimacs/049/01","DOIUrl":"https://doi.org/10.1090/dimacs/049/01","url":null,"abstract":"In this paper, we continue the study of acyclic improper colourings of graphs introduced in a previous work. An improper colouring of a graph G is a mapping c from the set of vertices of G to a set of colours such that for every colour i, the subgraph induced by the vertices with colour i satisses some property depending on i. Such an improper colouring is acyclic if for every two distinct colours i and j, the subgraph induced by all the edges linking an i-coloured vertex and a j-coloured vertex is acyclic. We consider in this paper the case of graphs with bounded degree. We prove some positive and negative results for graphs with maximum degree three and generalize some of the negative results to graphs with maximum degree k.","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126983675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the maximum lengths of Davenport-Schinzel sequences","authors":"Martin Klazar","doi":"10.1090/dimacs/049/11","DOIUrl":"https://doi.org/10.1090/dimacs/049/11","url":null,"abstract":"The quantity N5(n) is the maximum length of a finite sequence over n symbols which has no two identical consecutive elements and no 5-term alternating subsequence. Improving the constant factor in the previous bounds of Hart and Sharir, and of Sharir and Agarwal, we prove that N5(n) < 2nα(n) +O(nα(n) ), where α(n) is the inverse to the Ackermann function. Quantities Ns(n) can be generalized and any finite sequence, not just an alternating one, can be assigned extremal function. We present a sequence with no 5-term alternating subsequence and with an extremal function n2.","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126468812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Fekete, Winfried Hochstättler, S. Kromberg, Christoph Moll
{"title":"The complexity of an inverse shortest paths problem","authors":"S. Fekete, Winfried Hochstättler, S. Kromberg, Christoph Moll","doi":"10.1090/dimacs/049/06","DOIUrl":"https://doi.org/10.1090/dimacs/049/06","url":null,"abstract":"","PeriodicalId":144845,"journal":{"name":"Contemporary Trends in Discrete Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132643286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
求助内容：
应助结果提醒方式：