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991.
The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields components. Determining toughness is an NP‐hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K2‐free graphs, that is, graphs that do not contain two vertex‐disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K2‐free graphs. 相似文献
992.
Ya‐Chen Chen 《Journal of Graph Theory》2014,76(4):309-322
A graph is K2, 3‐saturated if it has no subgraph isomorphic to K2, 3, but does contain a K2, 3 after the addition of any new edge. We prove that the minimum number of edges in a K2, 3‐saturated graph on vertices is sat. 相似文献
993.
994.
We state and prove a general Harnack inequality for minimizers of nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p-Laplacian. 相似文献
995.
Piotr Gwiazda Agnieszka Świerczewska-Gwiazda Petra Wittbold Aleksandra Zimmermann 《Journal of Functional Analysis》2014
We consider scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect to both the space variable x and the unknown quantity u. We formulate the definition of entropy weak solutions and provide existence and uniqueness to the considered problem. The problem is formulated in the framework of multi-valued mappings. The notion of entropy measure-valued solutions is used to prove the so-called contraction principle and comparison principle. 相似文献
996.
997.
998.
We show how a theorem about the solvability in C1,1 of special Isaacs equations can be used to obtain existence and uniqueness of viscosity solutions of general uniformly nondegenerate Isaacs equations. We apply it also to establish the C1+χ regularity of viscosity solutions and show that finite-difference approximations have an algebraic rate of convergence. The main coefficients of the Isaacs equations are supposed to be in Cγ with γ slightly less than 1/2. 相似文献
999.
Let X be a Banach space and L the generator of the evolution semigroup associated with the τ -periodic evolutionary process {U(t,s)}t≥s on the space Pτ(X) of all τ-periodic continuous X -valued functions. We give criteria for the existence of periodic solutions to nonlinear systems of the form Lp=−?F(p,?) under the condition that 1 is a normal eigenvalue of the monodromy operator U(τ,0). The proof is based on a new decomposition of the space Pτ(X) by constructing a right inverse of L. 相似文献
1000.