The Dissimilarity Characteristic of Linear Graphs
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Motivated by the definition of linear coloring on simplicial complexes, recently introduced in the context of algebraic topology [9], and the framework through which it was studied, we introduce the linear coloring on graphs. We provide an upper bound for the chromatic number χ(G
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A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (@) or crossing (G). Given a family of linear graphs, and a non-empty subset R ⊆ {<, @, G} of these three relations, we are inter
A linear graph is a graph whose vertices are linearly ordered. This linear ordering allows pairs of disjoint edges to be either preceding (<), nesting (⊏) or crossing (≬). Given a family of linear graphs, and a non-empty subset R ⊆ {<,⊏, ≬}, we are interested in the MCSP problem: