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For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
Open problems on word-representable graphs can be found in, [3] [8] [9] [10] and they include: Characterise (non-)word-representable planar graphs. Characterise word-representable near-triangulations containing the complete graph K 4 (such a characterisation is known for K 4-free planar graphs [17]). Classify graphs with representation number 3.
The road coloring problem is the problem of edge-coloring a directed graph with uniform out-degrees, in such a way that the resulting automaton has a synchronizing word. Trahtman (2009) solved the road coloring problem by proving that such a coloring can be found whenever the given graph is strongly connected and aperiodic .
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. This is a gallery of curves ...
Mixed graphs are also used as graphical models for Bayesian inference. In this context, an acyclic mixed graph (one with no cycles of directed edges) is also called a chain graph. The directed edges of these graphs are used to indicate a causal connection between two events, in which the outcome of the first event influences the probability of ...
The r/dataisbeautiful subreddit requires users submitting visualizations to clearly credit both the individual who created the visualization and the source of the data on which it is based. If someone submits a visualization they created themselves, the rules require them to put "[OC]" in the title of the submission, and to identify the source ...
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]
Graphic representation of a minute fraction of the WWW, demonstrating hyperlinks.. Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
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