On critical subgraphs of colour-critical graphs
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It is proved that if a 4-critical graph I' has a vortex x of large valency (compared to the number of vertices of I' not adjacent to x), then I' contains Vertices of valency 3, and a list of all 4- critical graphs with @? 9 vertices is exhibited.About:
This article is published in Discrete Mathematics.The article was published on 1974-01-01 and is currently open access. It has received 39 citations till now. The article focuses on the topics: Chordal graph & Indifference graph.read more
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Graph Coloring Problems
Tommy R. Jensen,Bjarne Toft +1 more
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
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Hajós' graph-coloring conjecture: Variations and counterexamples
TL;DR: It is shown that a graph with chromatic number 4 contains as a subgraph a subdivided K4 in which each triangle of the K4 is subdivided to form an odd cycle.
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The Graph Coloring Problem: A Bibliographic Survey
TL;DR: In this article, an arbitrary undirected graph without loops is defined as a graph where V = {v 1, v 2,…, v n } is its vertex set and E = {e 1,e 2, e m } ⊂ (E ×E) is its edge set.
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Graph coloring and the immersion order
TL;DR: It is proved that minimal counterexamples must, if any exist, be both 4-vertex-connected and t-edge-connected, and the relationship between graph coloring and the immersion order is considered.
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Five-Coloring Graphs on the Torus
TL;DR: It is proved that a graph on the torus is 5-colorable, unless it contains either K6 the complete graph on six vertices, or C3 + C5, the join of two cycles of lengths three and five, respectively.
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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.
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On cliques in graphs
J. W. Moon,L. Moser +1 more
TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.