Local colourings and monochromatic partitions in complete bipartite graphs
نویسندگان
چکیده
We show that for any 2-local colouring of the edges of a complete bipartite graph, its vertices can be covered with at most 3 disjoint monochromatic paths. And, we can cover almost all vertices of any complete or complete bipartite r-locally coloured graph with O(r) disjoint monochromatic cycles. MSC: 05C38, 05C55.
منابع مشابه
Partitioning two-coloured complete multipartite graphs into monochromatic paths
We show that any complete k-partite graph G on n vertices, with k ≥ 3, whose edges are two-coloured, can be covered by two vertex-disjoint monochromatic paths of distinct colours, under the necessary assumption that the largest partition class of G contains at most n/2 vertices. This extends known results for complete and complete bipartite graphs. Secondly, we show that in the same situation, ...
متن کاملMonochromatic Cycle Partitions in Local Edge Colourings
An edge colouring of a graph is said to be an r-local colouring if the edges incident to any vertex are coloured with at most r colours. Generalising a result of Bessy and Thomassé, we prove that the vertex set of any 2-locally coloured complete graph may be partitioned into two disjoint monochromatic cycles of different colours. Moreover, for any natural number r, we show that the vertex set o...
متن کاملMonochromatic bounded degree subgraph partitions
Let F = {F1, F2, . . .} be a sequence of graphs such that Fn is a graph on n vertices with maximum degree at most ∆. We show that there exists an absolute constant C such that the vertices of any 2-edge-colored complete graph can be partitioned into at most 2C∆log ∆ vertex disjoint monochromatic copies of graphs from F . If each Fn is bipartite, then we can improve this bound to 2C∆; this resul...
متن کاملRECONFIGURING k-COLOURINGS OF COMPLETE BIPARTITE GRAPHS
Let H be a graph, and k ≥ χ(H) an integer. We say that H has a Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings (including the last and the first) agree on all vertices of H except one. The Gray code number of H is the least integer k0(H) such that H has a Gray code of its k-colourings for all k ≥ k0(H). For complete ...
متن کاملMixing 3-Colourings in Bipartite Graphs
For a 3-colourable graph G, the 3-colour graph of G, denoted C3(G), is the graph with node set the proper vertex 3-colourings of G, and two nodes adjacent whenever the corresponding colourings differ on precisely one vertex of G. We consider the following question : given G, how easily can we decide whether or not C3(G) is connected? We show that the 3-colour graph of a 3-chromatic graph is nev...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 60 شماره
صفحات -
تاریخ انتشار 2015