Sagnik Sen

Learn 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)
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)
A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the X-axis, distance 1 + (0 < < 1) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of(More)
As an extension of the Four-Color Theorem it is conjectured that every planar graph of odd-girth at least 2k + 1 admits a homomorphism to P C 2k = (Z 2k 2 , {e 1 , e 2 , · · · , e 2k , J}) where e i 's are standard basis and J is all 1 vector. Noting that P C 2k itself is of odd-girth 2k + 1, in this work we show that if the conjecture is true, then P C 2k(More)
To push a vertex v of a directed graph − → G is to change the orientations of all the arcs incident with v. An oriented graph is a directed graph without any cycle of length at most 2. An oriented clique is an oriented graph whose non-adjacent vertices are connected by a directed 2-path. A push clique is an oriented clique that remains an oriented clique(More)