We consider graphs G with ∆ = 3 such that χ′(G) = 4 and χ′(G− e) = 3 for every edge e, so-called critical graphs. Jakobsen noted that the Petersen graph with a vertex deleted, P ∗, is such a graph and has average degree only 2 + 2 3 . He showed that every critical graph has average degree at least 2+ 23 , and asked if P ∗ is the only graph where equality holds. We answer his question affirmativ...

The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions that are analogous to the famed version of the classical Littlewood-Richardson rule involving Yamanouchi words. Furthermore, both our rules contain this classical Littlewood...

The break minimization problem is to find a home-away assignment that minimizes the number of breaks for a given schedule of a round-robin tournament. In a recent paper, Elf et al. conjectured that this minimization problem is solvable in polynomial time if the optimal value of a given instance is less than the number of teams of the instance. We prove their conjecture affirmatively by showing ...

We propose a new identification scheme from a newly introduced lattice problem. Our scheme is a provable identification problem based on a lattice problem. This affirmatively answers the question raised by Hoffstein and others on the possibility to construct a provable identification/signature scheme from lattice problems. We give a concrete realization of the identification scheme using the NT...

Kim, C. and D.H. Lee, Separating k-separated eNCE graph languages, Theoretical Computer Science 120 (1993) 247-259. An eNCE graph grammar is k-separated (k > 1) if the distance between any two nonterminal nodes in any of its sentential forms is at least k. Let SEP, denote the class of graph languages generated by SEPl (SEP2) is the class of eNCE (boundar E) graph languages, Recently, Engelfriet...

Given n weighted points (positive or negative) in d dimensions, what is the axis-aligned box which maximizes the total weight of the points it contains? The best known algorithm for this problem is based on a reduction to a related problem, the Weighted Depth problem [Chan, FOCS, 2013], and runs in time O(n). It was conjectured [Barbay et al., CCCG, 2013] that this runtime is tight up to subpol...

INTRODUCTION..................................................................................................... 1325 I. CONTRACTING AT THE IPO STAGE ................................................................. 1331 A. IPO Charters and Takeover Defenses ...................................................... 1332 B. Innovation, Diversity, and the “Plain Vanilla” Charter ......................

Hearing impairment is common among the elderly and it compromises communication with resultant poor psychological functioning in affected individuals of all ages. To describe, age gender, literacy and residency status associated with self reported hearing difficulty in adults and its prevalence in Pakistan, we used data from the National Health Survey of Pakistan (NHSP) 1990-94; with written pe...

We determine the limiting distribution of the maximum vertex degree 2n in a random triangulation of an n-gon, and show that it is the same as that of the maximum of n independent identically distributed random variables G2 , where G2 is the sum of two independent geometric(1 2) random variables. This answers affirmatively a question of Devroye, Flajolet, Hurtado, Noy and Steiger, who gave much ...