Journal ArticleDOI
Maximum k-colorable subgraphs
Reads0
Chats0
TLDR
A lower bound is established on the number of edges in a maximum k-colorable subgraph of a loopless graph G that is a bipartite subgraph whose color classes are of equal size.Abstract:
A lower bound is established on the number of edges in a maximum k-colorable subgraph of a loopless graph G. For the special case of 3-regular graphs, lower bounds are also determined on the maximum number of edges in a bipartite subgraph whose color classes are of equal size.read more
Citations
More filters
Journal ArticleDOI
Problems and results on judicious partitions
Béla Bollobás,Alex Scott +1 more
TL;DR: It is shown that partitions of graphs or hypergraphs, where the objective is to maximize or minimize several quantities simultaneously, have algorithmic counterparts in a number of domains.
Journal ArticleDOI
Largest bipartite subgraphs in triangle-free graphs with maximum degree three
J. A. Bondy,Stephen C. Locke +1 more
TL;DR: In this article, an algorithm polynomial for determining a bipartite sous-graphe bipartitio d'un graphe G without triangle and a Boucle de degre maximum 3, contenant au moins 4/5 des aretes de G.
Journal ArticleDOI
Exact Bounds for Judicious Partitions of Graphs
Béla Bollobás,Alex Scott +1 more
TL;DR: It is shown that every graph of size has a bipartition in which the Edwards bound holds, and in addition each vertex class contains at most edges.
Book ChapterDOI
Judicious partitions and related problems.
TL;DR: In this survey, recent extremal results on a variety of questions concerning judicious partitions, and related problems such as Max Cut are discussed.
Book ChapterDOI
Parameters of Partial Orders and Graphs: Packing, Covering, and Representation
TL;DR: In this article, a survey of packing/covering parameters and representation parameters of graphs and posets is presented, starting from the poset parameters known as width and dimension, and generalizations, related ques¬tions, and analogous parameters for graphs and/or directed graphs.
References
More filters
Journal ArticleDOI
On Colouring the Nodes of a Network
TL;DR: Let N be a network (or linear graph) such that at each node not more than n lines meet (where n > 2), and no line has both ends at the same node.
Journal ArticleDOI
Some Extremal Properties of Bipartite Subgraphs
TL;DR: Gp = (V, X) is a graph on p vertices, with vertex set V and edge set X as discussed by the authors, where V and X will be written V(GP) and X(GP), respectively.
Journal ArticleDOI
On some extremal problems in graph theory
TL;DR: In this article, it was shown that if C is a sufficiently large constant, then every graph of n vertices and [Cn====== 3/2] edges contains a hexagon.
Journal ArticleDOI
Extremal bipartite subgraphs of cubic triangle‐free graphs
Glenn Hopkins,William Staton +1 more
TL;DR: A cubic triangle-free graph has a bipartite subgraph with at least 4/5 of the original edges with a best possible result.
Related Papers (5)
Largest bipartite subgraphs in triangle-free graphs with maximum degree three
J. A. Bondy,Stephen C. Locke +1 more