Hamilton cycles in almost distance-hereditary graphs

Let $G$ be a graph on $n\geq 3$ vertices. A graph $G$ is almost distance-hereditary if each connected induced subgraph $H$ of $G$ has the property $d_{H}(x,y)\leq d_{G}(x,y)+1$ for any pair of vertices $x,y\in V(H)$. A graph $G$ is called 1-heavy (2-heavy) if at least one (two) of the end vertices of each induced subgraph of $G$ isomorphic to $K_{1,3}$ (a claw) has (have) degree at least $n/2$, and called claw-heavy if each claw of $G$ has a pair of end vertices with degree sum at least $n$. Thus every 2-heavy graph is claw-heavy. In this paper we prove the following two results: (1) Every 2-connected, claw-heavy and almost distance-hereditary graph is Hamiltonian. (2) Every 3-connected, 1-heavy and almost distance-hereditary graph is Hamiltonian. In particular, the first result improves a previous theorem of Feng and Guo. Both results are sharp in some sense.Comment: 14 pages; 1 figure; a new theorem is adde

On Timing Model Extraction and Hierarchical Statistical Timing Analysis

In this paper, we investigate the challenges to apply Statistical Static Timing Analysis (SSTA) in hierarchical design flow, where modules supplied by IP vendors are used to hide design details for IP protection and to reduce the complexity of design and verification. For the three basic circuit types, combinational, flip-flop-based and latch-controlled, we propose methods to extract timing models which contain interfacing as well as compressed internal constraints. Using these compact timing models the runtime of full-chip timing analysis can be reduced, while circuit details from IP vendors are not exposed. We also propose a method to reconstruct the correlation between modules during full-chip timing analysis. This correlation can not be incorporated into timing models because it depends on the layout of the corresponding modules in the chip. In addition, we investigate how to apply the extracted timing models with the reconstructed correlation to evaluate the performance of the complete design. Experiments demonstrate that using the extracted timing models and reconstructed correlation full-chip timing analysis can be several times faster than applying the flattened circuit directly, while the accuracy of statistical timing analysis is still well maintained

The meson-exchange model for the ΛΛˉ\Lambda\bar{\Lambda} interaction

In the present work, we apply the one-boson-exchange potential (OBEP) model to investigate the possibility of Y(2175) and $\eta(2225)$ as bound states of $\Lambda\bar{\Lambda}(^3S_1)$ and $\Lambda\bar{\Lambda}(^1S_0)$ respectively. We consider the effective potential from the pseudoscalar $\eta$-exchange and $\eta^{'}$-exchange, the scalar $\sigma$-exchange, and the vector $\omega$-exchange and $\phi$-exchange. The $\eta$ and $\eta^{'}$ meson exchange potential is repulsive force for the state $^1S_0$ and attractive for $^3S_1$. The results depend very sensitively on the cutoff parameter of the $\omega$-exchange ($\Lambda_{\omega}$) and least sensitively on that of the $\phi$-exchange ($\Lambda_{\phi}$). Our result suggests the possible interpretation of Y(2175) and $\eta(2225)$ as the bound states of $\Lambda\bar{\Lambda}(^3S_1)$ and $\Lambda\bar{\Lambda}(^1S_0)$ respectively