Heavy subgraphs, stability and hamiltonicity

Let $G$ be a graph. Adopting the terminology of Broersma et al. and \v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is o-heavy if every induced claw of $G$ contains two end-vertices with degree sum at least $|V(G)|$ in $G$. In this paper, we introduce a new concept, and say that $G$ is \emph{$S$-c-heavy} if for a given graph $S$ and every induced subgraph $G'$ of $G$ isomorphic to $S$ and every maximal clique $C$ of $G'$, every non-trivial component of $G'-C$ contains a vertex of degree at least $|V(G)|/2$ in $G$. In terms of this concept, our original motivation that a theorem of Hu in 1999 can be stated as every 2-connected 2-heavy and $N$-c-heavy graph is hamiltonian, where $N$ is the graph obtained from a triangle by adding three disjoint pendant edges. In this paper, we will characterize all connected graphs $S$ such that every 2-connected o-heavy and $S$-c-heavy graph is hamiltonian. Our work results in a different proof of a stronger version of Hu's theorem. Furthermore, our main result improves or extends several previous results.Comment: 21 pages, 6 figures, finial version for publication in Discussiones Mathematicae Graph Theor

Sistesis aliran ekuivalen tree dengan menggunakan algoritma gomary - hu

ABSTRAK Suatu jaringan komunikasi tak berarah G(V, E, c, f) merupakan suatu jaringan komunikasi dengan himpunan titik V, himpunan garis E, fungsi kapasitas c dan fungsi aliran f. Dalam jaringan komunikasi ini, medium antar dua station yang dalam hal ini digambarkan sebagai garis mempunyai kapasitas yang disebut sebagai kapasitas garis. Dad kapasitas garis ini dapat ditentukan kapasitas terminalnya. Setiap jaringan komunikasi tak berarah -n-titik adalah ekuivalen terhadap tree dan terdapat paling banyak n - 1 bilangan kapasitas terminal yang berbeda. Algoritma Gomory - Hu membangun jaringan yang ekuivalen terhadap tree dengan menyelesaikan secara tepat masalah aliran maksimum n - 9. Masalah aliran maksimum ini diselesaikan daiam suatu jaringan yang lebih sederhana daripada jaringan asli

Barriers to Pediatric Sickle Cell Disease Guideline Recommendations.

National guidelines recommend that providers counsel all patients with sickle cell anemia about hydroxyurea (HU) therapy and screen children with sickle cell anemia annually for the risk of stroke with transcranial Doppler (TCD). We surveyed a national convenience sample of sickle cell disease clinicians to assess factors associated with low adherence. Adherence was 46% for TCD screening. Low adherence was associated with a lack of outcome expectancy (eg, a belief that there would be poor patient follow-up to TCD testing; P < .05). Adherence was 72% for HU counseling. Practice barriers (eg, lack of support staff or time) and a lack of agreement with HU recommendations were associated with low adherence (P < .05). This study demonstrates that different types of strategies are needed to improve TCD screening (to address follow-up and access to testing) versus HU counseling (to address physician agreement and practice barriers)

Optimal Alphabetic Ternary Trees

We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to be determined

Alternative Derivation of the Hu-Paz-Zhang Master Equation for Quantum Brownian Motion

Hu, Paz and Zhang [ B.L. Hu, J.P. Paz and Y. Zhang, Phys. Rev. D {\bf 45} (1992) 2843] have derived an exact master equation for quantum Brownian motion in a general environment via path integral techniques. Their master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In this paper, we give an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evolution equation for the Wigner function. We also discuss the master equation in some special cases.Comment: 17 pages, Revte