We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
Wang and Lih conjectured that for every g 5, there exists a number M(g) such that the square of a planar graph G of girth at least g and maximum degree M(g) is (+1)-colorable. ...
The Colorful Motif problem asks if, given a vertex-colored graph G, there exists a subset S of vertices of G such that the graph induced by G on S is connected and contains every c...
Abhimanyu M. Ambalath, Radheshyam Balasundaram, Ch...
We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n)....
We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree . We prove that, for every > 0, the d...
Martin E. Dyer, Alan M. Frieze, Thomas P. Hayes, E...