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71.
Let G be a connected graph. For ${x,y\in V(G)}$ with d(x, y) = 2, we define ${J(x,y)= \{u \in N(x)\cap N(y)\mid N[u] \subseteq N[x] \,{\cup}\,N[y] \}}$ and ${J'(x,y)= \{u \in N(x) \cap N(y)\,{\mid}\,{\rm if}\ v \in N(u){\setminus}(N[x] \,{\cup}\, N[y])\ {\rm then}\ N[x] \,{\cup}\, N[y]\,{\cup}\,N[u]{\setminus}\{x,y\}\subseteq N[v]\}}$ . A graph G is quasi-claw-free if ${J(x,y) \not= \emptyset}$ for each pair (x, y) of vertices at distance 2 in G. Broersma and Vumar (in Math Meth Oper Res. doi:10.1007/s00186-008-0260-7) introduced ${\mathcal{P}_{3}}$ -dominated graphs defined as ${J(x,y)\,{\cup}\, J'(x,y)\not= \emptyset}$ for each ${x,y \in V(G)}$ with d(x, y) = 2. This class properly contains that of quasi-claw-free graphs, and hence that of claw-free graphs. In this note, we prove that a 2-connected ${\mathcal{P}_3}$ -dominated graph is 1-tough, with two exceptions: K 2,3 and K 1,1,3, and prove that every even connected ${\mathcal{P}_3}$ -dominated graph ${G\ncong K_{1,3}}$ has a perfect matching. Moreover, we show that every even (2p + 1)-connected ${\mathcal{P}_3}$ -dominated graph is p-extendable. This result follows from a stronger result concerning factor-criticality of ${\mathcal{P}_3}$ -dominated graphs. 相似文献
72.
73.
74.
In this paper, we give a necessary condition for the existence of P
3-factor in the square of a tree. Furthermore, we show that the square of any tree on at least 6 vertices has a {P
3,P
4}-factor. As a consequence, every connected graph on at least 6 vertices has a {P
3,P
4}-factor.
Zhao Zhang: The research is supported by NSFC (60603003) and XJEDU.
Received: November 15, 2006. Final version received: December 12, 2007. 相似文献
75.
Turdebek N. Bekjan 《Journal of Functional Analysis》2008,254(9):2401-2418
Let M be a von Neumann algebra equipped with a normal semifinite faithful trace τ. Let T be a positive linear contraction on M such that τ○T?τ and such that the numerical range of T as an operator on L2(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on Lp(M), 1<p?∞. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations. 相似文献
76.
Let A(G) be the adjacency matrix of G. The characteristic polynomial of the adjacency matrix A is called the characteristic polynomial of the graph G and is denoted by φ(G, λ) or simply φ(G). The spectrum of G consists of the roots (together with their multiplicities) λ 1(G) ? λ 2(G) ? … ? λ n (G) of the equation φ(G, λ) = 0. The largest root λ 1(G) is referred to as the spectral radius of G. A ?-shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by G(l 1, l 2, … l 7) (l 1 ? 0, l i ? 1, i = 2, 3, …, 7) a ?-shape tree such that $G\left( {l_1 ,l_2 , \ldots l_7 } \right) - u - v = P_{l_1 } \cup P_{l_2 } \cup \ldots P_{l_7 }$ , where u and v are the vertices of degree 4. In this paper we prove that ${{3\sqrt 2 } \mathord{\left/ {\vphantom {{3\sqrt 2 } 2}} \right. \kern-0em} 2} < \lambda _1 \left( {G\left( {l_1 ,l_2 , \ldots l_7 } \right)} \right) < {5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-0em} 2}$ . 相似文献
77.
研究了由加权Lipschitz函数b和Calderón-Zygmund奇异积分算子T生成的交换子Tb在一些加权空间上的有界性,涉及到加权Hardy空间,加权Herz空间及和加权Herz型Hardy空间.同时也得到了其相应的端点估计. 相似文献
78.
79.
《Physics letters. A》1999,252(6):297-306
We introduce a nonlinear dispersive quintic equation. Its travelling waves are governed by a linear equation. We construct a large variety of explicit compact solitary waves. Some of these compactons are very robust, others decompose very quickly. Numerical simulations also reveal the existence of compact travelling breathers. 相似文献
80.
In this paper, the boundedness of mulitilinear commutator [b,T] on Herz-type space is considered, where T is a standard Calderón-Zygmund singular operator and b ∈ (BMO(Rn))m. 相似文献