
The chromatic number of 2edgecolored and signed graphs of bounded maximum degree
A 2edgecolored graph or a signed graph is a simple graph with two type...
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Signified chromatic number of grids is at most 9
A signified graph is a pair (G, Σ) where G is a graph, and Σ is a set of...
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Property Graph Type System and Data Definition Language
Property graph manages data by vertices and edges. Each vertex and edge ...
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The chromatic number of signed graphs with bounded maximum average degree
A signed graph is a simple graph with two types of edges: positive and n...
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Embedding of Hypercube into Cylinder
Task mapping in modern high performance parallel computers can be modele...
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Robotic Mapping with Polygonal Random Fields
Two types of probabilistic maps are popular in the mobile robotics liter...
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VertexDomatic, EdgeDomatic and Total Domatic Number of Uniform Hypergraphs
E. J. Cockayne and S. T. Hedetniemi introduced the concept of domatic nu...
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On the chromatic numbers of signed triangular and hexagonal grids
A signed graph is a simple graph with two types of edges. Switching a vertex v of a signed graph corresponds to changing the type of each edge incident to v. A homomorphism from a signed graph G to another signed graph H is a mapping φ: V(G) → V(H) such that, after switching any number of the vertices of G, φ maps every edge of G to an edge of the same type in H. The chromatic number χ_s(G) of a signed graph G is the order of a smallest signed graph H such that there is a homomorphism from G to H. We show that the chromatic number of signed triangular grids is at most 10 and the chromatic number of signed hexagonal grids is at most 4.
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