Minimum Cycle Base of Graphs Identified by Two Planar Graphs

In this paper, we study the minimum cycle base of the planar graphs obtained from two 2-connected planar graphs by identifying an edge (or a cycle) of one graph with the corresponding edge (or cycle) of another, related with map geometries, i.e., Smarandache 2-dimensional manifolds

Shortest Co-cycle Bases of Graphs

In this paper we investigate the structure of the shortest co-cycle base(or SCB in short) of connected graphs, which are related with map geometries, i.e., Smarandache 2-dimensional manifolds. By using a Hall type theorem for base transformation, we show that the shortest co-cycle bases have the same structure (there is a 1-1 correspondence between two shortest co-cycle bases such that the corresponding elements have the same length). As an application in surface topology, we show that in an embedded graph on a surface any nonseparating cycle can’t be generated by separating cycles. Based on this result, we show that in a 2-connected graph embedded in a surface, there is a set of surface nonseparating cycles which can span the cycle space. In particular, there is a shortest base consisting surface nonseparating cycle and all such bases have the same structure. This extends a Tutte’s result

Exploiting h→W∗W∗h \to W^*W^* Decays at the Upgraded Fermilab Tevatron

We study the observability of a Standard Model-like Higgs boson at an upgraded Fermilab Tevatron via the mode $h \to W^*W^*$. We concentrate on the main channel $gg \to h \to W^*W^* \to l \nu l \nu$. We also find the mode $q\bar q'\to W h \to W W^*W^* \to l^\pm \nu l^\pm \nu jj$ useful. We perform detector level simulations by making use of a Monte Carlo program SHW. Optimized searching strategy and kinematical cuts are developed. We find that with a c.m. energy of 2 TeV and an integrated luminosity of 30 fb$^{-1}$ the signal should be observable at a 3$\sigma$ level or better for the mass range of 145 GeV < m_h < 180 GeV. For 95% confidence level exclusion, the mass reach is 135 GeV < m_h <190 GeV. We also present results of studying these channels with a model-independent parameterization. Further improvement is possible by including other channels. We conclude that the upgraded Fermilab Tevatron will have the potential to significantly advance our knowledge of Higgs boson physics.Comment: 23 pages; 15 figures; 5 table