共查询到13条相似文献,搜索用时 0 毫秒
1.
A unichord is an edge that is the unique chord of a cycle in a graph. The class C of unichord-free graphs — that is, graphs that do not contain, as an induced subgraph, a cycle with a unique chord — was recently studied by Trotignon and Vuškovi? (2010) [24], who proved strong structure results for these graphs and used these results to solve the recognition and vertex-colouring problems. Machado et al. (2010) [18] determined the complexity of the edge-colouring problem in the class C and in the subclass C′ obtained from C by forbidding squares. In the present work, we prove that the total-colouring problem is NP-complete when restricted to graphs in C. For the subclass C′, we establish the validity of the Total Colouring Conjecture by proving that every non-complete {square, unichord}-free graph of maximum degree at least 4 is Type 1. 相似文献
2.
In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic σ≤ 0 is given, that generalizes a result of Borodin on plane graphs. As a consequence, it is proved that every such graph without i-circuits for 4 ≤ i ≤ 11 - 3σ is 3-choosable, that offers a new upper bound to a question of Y. Zhao. 相似文献
3.
4.
A structural theorem for planar graphs with some applications 总被引:1,自引:0,他引:1
Huiyu ShengYingqian Wang 《Discrete Applied Mathematics》2011,159(11):1183-1187
In this note, we prove a structural theorem for planar graphs, namely that every planar graph has one of four possible configurations: (1) a vertex of degree 1, (2) intersecting triangles, (3) an edge xy with d(x)+d(y)≤9, (4) a 2-alternating cycle. Applying this theorem, new moderate results on edge choosability, total choosability, edge-partitions and linear arboricity of planar graphs are obtained. 相似文献
5.
A total k-coloring of a graph G is a coloring of V(G) ∪ E(G) using k colors such that no two adjacent or incident elements receive the same color. The total chromatic number χ'(G) is the smallest integer k such that G has a total k-coloring. It is known that if a planar graph G has maximum degree Δ≥ 9, then χ'(G) = Δ + 1. In this paper, we prove that if G is a planar graph with maximum degree 8 and without a fan of four adjacent 3-cycles, then χ'(G) = 9. 相似文献
6.
J. Plávka 《Mathematical Methods of Operations Research》1992,36(5):417-422
Let twon×n matrices be given, namely a real matrixA=(aij) and a (0, 1)-matrixT=(tij). For a cyclic permutation=(i
1,i
2,...,i
k) of a subset of N={1, 2, ..., n} we define A;T(), the cost-to-time ratio weight of, as
. This paper presents an O(n3) algorithm for finding (A;T)=max A;T(), the maximum cost-to-time ratio weight of the matricesA andT. Moreover a generalised eigenproblem is proposed. 相似文献
7.
Hatem Zaag 《纯数学与应用数学通讯》2001,54(1):107-133
We prove a Liouville theorem for the following heat system whose nonlinearity has no gradient structure: where pq, > 1, p ≥ 1, q ≥ 1, and |p−q| small. We then deduce a localization property and uniform L∞ estimates of blowup solutions of this system. © 2001 John Wiley & Sons, Inc. 相似文献
8.
Ioannis K. Argyros 《Journal of Complexity》2011,27(1):39-54
We present a semilocal convergence theorem for Newton’s method (NM) on spaces with a convergence structure. Using our new idea of recurrent functions, we provide a tighter analysis, with weaker hypotheses than before and with the same computational cost as for Argyros (1996, 1997, 1997, 2007) [1], [2], [3] and [5], Meyer (1984, 1987, 1992) [13], [14] and [15]. Numerical examples are provided for solving equations in cases not covered before. 相似文献
9.
Phan Thien Thach 《Mathematical Programming》1992,53(1-3):339-359
In this paper we develop a decomposition method using a pricing mechanism which has been widely applied to linear and convex programs for a class of nonconvex optimization problems that are min concave cost flow problems under directed, uncapacitated networks with a hierarchical structure.This paper was completed during the author's stay supported by a Sophia lecturing-research Grant at Sophia University, Tokyo, Japan. 相似文献
10.
杨贺菊 《数学的实践与认识》2010,40(2)
首先利用积分方程的方法和Arzela-Ascoli定理讨论了实Clifford分析中双正则函数向量的带Haseman位移带共轭值的非线性边值问题解的存在性及其积分表达式,其次利用压缩映射原理解决了其线性边值问题解的存在唯一性及其积分表达式. 相似文献
11.
Time-discrete systems with a finite set of states are considered. Discrete optimal control problems with infinite time horizon
for such systems are formulated. We introduce a certain graph-theoretic structure to model the transitions of the dynamical
system. Algorithms for finding the optimal stationary control parameters are presented. Furthermore, we determine the optimal
mean cost cycles. This approach can be used as a decision support strategy within such a class of problems; especially so-called
multilayered decision problems which occur within environmental emission trading procedures can be modelled by such an approach. 相似文献
12.
Kuo-Chih Hung 《Journal of Differential Equations》2011,251(2):223-237
We study the bifurcation curve and exact multiplicity of positive solutions of the positone problem
13.
Jonathan David Farley 《Discrete Mathematics》2007,307(2):191-198
Suppose a finite poset P is partitioned into three non-empty chains so that, whenever p, q∈P lie in distinct chains and p<q, then every other element of P is either above p or below q.In 1985, the following conjecture was made by David Daykin and Jacqueline Daykin: such a poset may be decomposed into an ordinal sum of posets such that, for 1?i?n, one of the following occurs:
- (1)
- Ri is disjoint from one of the chains of the partition; or
- (2)
- if p, q∈Ri are in distinct chains, then they are incomparable.