Clique covering and degree conditions for Hamiltonicity in claw-free graphs. (English summary) Graph theory (Kazimierz Dolny, 1997). Discrete Math. 236 (2001), no. 1-3, 65–80. Summary: “By using the closure concept introduced by the last author, we prove that for any sufficiently large non-Hamiltonian claw-free graph G satisfying a degree condition of type σk(G)&gt; n + k 2 − 4k + 7 (where k is a constant), the closure of G can be covered by at most k − 1 cliques. Using structural properties of the closure concept, we show a method for characterizing all such non-Hamiltonian exceptional graphs with limited clique covering number. The method is explicitly carried out for k ≤ 6 and illustrated by proving that every 2-connected claw-free graph G of order n ≥ 77 with δ(G) ≥ 14 and σ6(G)&gt; n + 19 either is Hamiltonian or belongs to a family of

Cited by 0

Language Reference

Mr (g: C, D. (-emry-cs) Sauer, N. W. (-calg-ms · 1997

Cited by 0

Language Reference

Mr (i: C, O. V. (rs-novo-im) Ivanova, A. O. (rs-yaku-rim · 1997

MR2408363 (2009b:05099)] that every planar graph with girth g ≥ 6 and maximum degree ∆ ≥ 8821 is 2-distance ( ∆ + 2)-colorable. We prove that every planar graph with g ≥ 6 and ∆ ≥ 18 is

Cited by 0

Language Reference

Mr (a: C, K. M. (sgp-sing) Ng, K. L. [ng et al. · 1997

Cited by 0

Language Reference

Mr (c: A (c, Alan S. (-nc) Techanie · 1997

Cited by 0

Language Reference

Mr (c: J (c, B. S. [mordukhovich, Boris S. (-wyns) Nam et al. · 1997

Fréchet subdifferential calculus and optimality conditions in nondifferentiable programming. (English summary) Optimization 55 (2006), no. 5-6, 685–708.1029-4945 The authors develop exact calculus rules for Fréchet subgradients and related concepts in real Banach spaces. They apply these calculus rules to obtain necessary optimality conditions for constrained problems involving DC functions (i.e. which are the difference of convex functions). Further applications are given to derive necessary conditions for weak sharp minimizers.

Cited by 0

Language Reference

Mr (b: C (c, József (h-aos) Bollobás, Béla (h-aos) Simonovits et al. · 1997

Cited by 0

Language Reference

Mr (f: C, Béla (-memp) Nikiforov, Vladimir S. (-memp et al. · 1997

Degree powers in graphs with forbidden subgraphs. (English summary) Electron. J. Combin. 11 (2004), no. 1, Research Paper 42, 8 pp. (electronic). The problem of minimizing the sum of (equal) powers of the degrees of the vertices of a graph with a given number of vertices and without a prescribed subgraph was treated by Y. Caro and

Cited by 0

Language Reference

Béla (-memp) Riordan · 1997

The critical probability for random Voronoi percolation in the plane is 1/2. (English summary) Probab. Theory Related Fields 136 (2006), no. 3, 417–468. This is a very good paper in which the result of the title is proven for Voronoĭ tessellations of a typical Poisson process in the plane. The main hurdle of extending Kesten’s famous result on bond percolation from the lattice Z 2 to this case is the absence of the Russo-Seymour-Welsh argument. The authors provide a slightly weaker statement which suffices for the proof, combined with sharp threshold results of E. Friedgut and G. Kalai [Proc. Amer. Math. Soc. 124 (1996), no. 10, 2993– 3002; MR1371123 (97e:05172)]. The paper is well written, and the authors have already extended their techniques and results to various related percolation models [Random Structures Algorithms 29 (2006), no. 4, 524–548; MR2268234 (2007h:60089)]. Reviewed by Aernout C. D. van Enter

Cited by 0

Language Reference

Mr C, Alon Noga (il-tlav, N. Eigenvalues · 1997

Cited by 0

Language Reference

Mr (i: C (c, Hassan (sar-upam) Biswas · 1997

Cited by 0

Language Reference

Mr (e: C, V. A. (d-tud-al) Pöschel, Reviewed Robert Jajcay et al. · 1997

Cited by 0

Language Reference

Mr (b: C, Michael T. (-sunys, Reviewed Bennett Chow · 1997

Scalar curvature and the existence of geometric structures on 3-manifolds. I. (English summary) J. Reine Angew. Math. 553 (2002), 125–182. Summary: “This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston’s geometrization conjecture. The sequences are minimizing sequences for a certain (optimal) scalar curvature-type functional and their degeneration is related to the sphere and torus decompositions of the 3-manifold under certain conditions.” The genesis of the idea of using the solutions to the Yamabe problem to approach the Poincaré Conjecture was originated by Yamabe and then developed further by Schoen, in terms of the minimax method, who also solved the long standing Yamabe problem using the positive mass theorem of Schoen and Yau, along with earlier works by Trudinger and Aubin.

Cited by 0

Language Reference

Mr (h: Q (c, Weiyue (prc-bj-mam) Tang, Hongyan (prc-tsi) Zeng · 1997

Cited by 0