For a graph G, it is known to be a hard problem to compute the competition number k(G) of the graph G in general. In this paper, we give an explicit formula for the competition nu...
Graph homomorphism, also called H-coloring, is a natural generalization of graph coloring: There is a homomorphism from a graph G to a complete graph on k vertices if and only if ...
We give a proof of Guenin's theorem characterizing weakly bipartite graphs by not having an odd-K5 minor. The proof curtails the technical and case-checking parts of Guenin...
We give a characterization for isoperimetric invariants, including the Cheeger constant and the isoperimetric number of a graph. This leads to an isoperimetric inequality for the ...
The richest class of t-perfect graphs known so far consists of the graphs with no so-called odd-K4. Clearly, these graphs have the special property that they are hereditary t-perfe...