On a Theorem of Erdos, Rubin, and Taylor on Choosability of Complete Bipartite Graphs
نویسنده
چکیده
Erdős, Rubin, and Taylor found a nice correspondence between the minimum order of a complete bipartite graph that is not r-choosable and the minimum number of edges in an r-uniform hypergraph that is not 2-colorable (in the ordinary sense). In this note we use their ideas to derive similar correspondences for complete kpartite graphs and complete k-uniform k-partite hypergraphs.
منابع مشابه
META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملAn Upper Bound for List T-colourings
Erdos, Rubin and Taylor showed in 1979 that for any connected graph G which is not a complete graph or an odd cycle, ch(G) < A, where A is the maximum degree of a vertex in G and ch(G) is the choice number of the graph (also proved by Vizing in 1976). They also gave a characterisation of Z)-choosability. A graph G is Z)-choosable if, when we assign to each vertex u o f G a list containing d(v) ...
متن کاملCircular consecutive choosability of graphs
Abstract This paper considers list circular colouring of graphs in which the colour list assigned to each vertex is an interval of a circle. The circular consecutive choosability chcc(G) of G is defined to be the least t such that for any circle S(r) of length r ≥ χc(G), if each vertex x of G is assigned an interval L(x) of S(r) of length t, then there is a circular r-colouring f of G such that...
متن کاملStar and Biclique Coloring and Choosability
A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic...
متن کاملBalanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 9 شماره
صفحات -
تاریخ انتشار 2002