Planck's law In 1880, André-Prosper-Paul Crova published a diagram of the three-dimensional appearance of the graph of the strength of thermal radiation as a function of wavelength and temperature. He determined the spectral variable by use of prisms. He analyzed the surface through what he called "isothermal" curves, sections for a single temperature, with a spectral variable on the abscissa and a power variable on the ordinate. He put smooth curves through his experimental data points. They had one peak at a spectral value characteristic for the temperature, and fell either side of it towards the horizontal axis. Such spectral sections are
Graph homomorphism can be solved by brute-force in time |"V"("H")|, so polynomial in the size of the input graph "H". In other words, the problem is trivially in P for graphs "G" of bounded size. The interesting question is then what other properties of "G", beside size, make polynomial algorithms possible. The crucial property turns out to be treewidth, a measure of how tree-like the graph is. For a graph "G" of treewidth at most "k" and a graph "H", the homomorphism problem can be solved in time |"V"("H")| with a standard dynamic programming approach. In fact, it is enough to assume