Edge and total choosability of near-outerplanar graphs

It is proved that, if G is a K4-minor-free graph with maximum degree ∆ ≥ 4, then G is totally (∆ + 1)-choosable; that is, if every element (vertex or edge) of G is assigned a list of ∆ + 1 colours, then every element can be coloured with a colour from its own list in such a way that every two adjacent or incident elements are coloured with different colours. Together with other known results, this shows that the List-Total-Colouring Conjecture, that ch’’(G) = χ’(G) for every graph G, is true for all K4-minor-free graphs. The List-Edge-Colouring Conjecture is also known to be true for these graphs. As a fairly straightforward consequence, it is proved that both conjectures hold also for all K2,3-minor free graphs and all ( K2 + (K1 U K2))-minor-free graphs

Detecting a light Higgs boson at the Fermilab Tevatron through enhanced decays to photon pairs

We analyze the prospects of the Tevatron for finding a Higgs boson in the two photon decay mode. We conclude that the Standard Model (SM) Higgs boson will likely not be discovered in this mode. However, we motivate several theories beyond the SM, including the MSSM, that predict a Higgs boson with enhanced branching fractions into photons, and calculate the luminosity needed to discover a general Higgs boson at the Tevatron by a two-photon invariant mass peak at large transverse momentum. We find that a high luminosity Tevatron will play a significant role in discovering or constraining these theories.Comment: 20 pages, latex, 5 figure