2nd CanaDAM Conference Open Problems
نویسندگان
چکیده
Open problems submitted to the 2nd Canadian Discrete and Algorithmic Mathematics Conference will be held on May 25-28, 2009, at the Centre de recherches mathématiques in Montréal, Canada. put brief summary here Comments and questions of a technical nature about a particular problem should be sent to the correspondent for that problem. Please send other comments and information about partial or full solutions to the organization committee for the next CanaDAM Conference. PROBLEM 1. Chemical Graph Theory: Maximum cardinality resonant sets and maximal alternating sets of hexagonal systems Khaled Salem The British University in Egypt [email protected] Let H be a hexagon system: that is, a 2-connected plane graph whose inner faces are all regular hexagons. Let P be a subset of the hexagons of H. If we can find a perfect matching M such that each of the hexagons of P intersects M in precisely three edges, then we say that P is a maximal alternating set. An M-resonant set S is a set of pairwise disjoint hexagons in H such that the boundary of each of the hexagons in S is alternating in M . Conjecture 1: Let H, P , M be given as defined. Then an M -resonant set of maximum cardinality is canonical, in the sense that if you delete the vertices of the M -resonant set from H, the remaining graph will either be empty or it will have a unique perfect matching. ∗School of Mathematics and Statistics, Carleton University, [email protected]
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