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We define and study a class of graphs, called 2-stab interval graphs (2SIG), with boxicity 2 which properly contains the class of interval graphs. A 2SIG is an axes-parallel rectangle intersection graph where the rectangles have unit height (that is, length of the side parallel to Y-axis) and intersects either of the two fixed lines, parallel to the X-axis,(More)
The clique number of an undirected graph G is the maximum order of a complete subgraph of G and is a well-known lower bound for the chromatic number of G. Every proper k-coloring of G may be viewed as a homomorphism (an edge-preserving vertex mapping) of G to the complete graph of order k. By considering homomorphisms of oriented graphs (digraphs without(More)
A (m, n)-colored mixed graph is a graph having arcs of m different colors and edges of n different colors. A graph homomorphism of a (m, n)-colored mixed graph G to a (m, n)-colored mixed graph H is a vertex mapping such that if uv is an arc (edge) of color c in G, then f (u)f (v) is also an arc (edge) of color c. The (m, n)-colored mixed chromatic number χ(More)