Backbone colorings along perfect matchings

Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V\rightarrow \{1,2,\ldots\}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least two. In a recent paper, backbone colorings were introduced and studied in cases were the backbone is either a spanning tree or a spanning path. Here we study the case where the backbone is a perfect matching. We show that for perfect matching backbones of $G$ the number of colors needed for a backbone coloring of $G$ can roughly differ by a multiplicative factor of at most $\frac{4}{3}$ from the chromatic number $\chi(G)$. We show that the computational complexity of the problem ``Given a graph $G$ with a perfect matching $M$, and an integer $\ell$, is there a backbone coloring for $G$ and $M$ with at most $\ell$ colors?'' jumps from polynomial to NP-complete between $\ell=3$ and $\ell=4$. Finally, we consider the case where $G$ is a planar graph

Toughness and hamiltonicity in kk-trees

We consider toughness conditions that guarantee the existence of a hamiltonian cycle in $k$-trees, a subclass of the class of chordal graphs. By a result of Chen et al.\ 18-tough chordal graphs are hamiltonian, and by a result of Bauer et al.\ there exist nontraceable chordal graphs with toughness arbitrarily close to $\frac{7}{4}$. It is believed that the best possible value of the toughness guaranteeing hamiltonicity of chordal graphs is less than 18, but the proof of Chen et al.\ indicates that proving a better result could be very complicated. We show that every 1-tough 2-tree on at least three vertices is hamiltonian, a best possible result since 1-toughness is a necessary condition for hamiltonicity. We generalize the result to $k$-trees for $k\ge 2$: Let $G$ be a $k$-tree. If $G$ has toughness at least $\frac{k+1}{3},$ then $G$ is hamiltonian. Moreover, we present infinite classes of nonhamiltonian 1-tough $k$-trees for each $k\ge 3

Prevalence of airflow limitation in outpatients with cardiovascular diseases in Japan.

Background and objectives: Cardiovascular disease (CVD) and chronic obstructive pulmonary disease (COPD) commonly coexist and share common risk factors. The prevalence of COPD in outpatients with a smoking history and CVD in Japan is unknown. The aim of this study was to determine the proportion of Japanese patients with a smoking history being treated for CVD who have concurrent airflow limitation compatible with COPD. A secondary objective was to test whether the usage of lung function tests performed in the clinic influenced the diagnosis rate of COPD in the patients identified with airflow limitation. Methods: In a multicenter observational prospective study conducted at 17 centers across Japan, the prevalence of airflow limitation compatible with COPD (defined as forced expiratory volume (FEV)1/FEV6 <0.73, by handheld spirometry) was investigated in cardiac outpatients ≥40 years old with a smoking history who routinely visited the clinic for their CVD. Each patient completed the COPD Assessment Test prior to spirometry testing. Results: Data were available for 995 patients with a mean age of 66.6±10.0 years, of whom 95.5% were male. The prevalence of airflow limitation compatible with COPD was 27.0% (n=269), and 87.7% of those patients (n=236) did not have a prior diagnosis of COPD. The prevalence of previously diagnosed airflow limitation was higher in sites with higher usage of lung function testing (14.0%, 15.2% respectively) compared against sites where it is performed seldom (11.1%), but was still low. Conclusion: The prevalence of airflow limitation in this study indicates that a quarter of outpatients with CVD have COPD, almost all of whom are undiagnosed. This suggests that it is important to look routinely for COPD in CVD outpatients

The relationship between the COPD Assessment Test score and airflow limitation in Japan in patients aged over 40 years with a smoking history.

BACKGROUND: A large number of chronic obstructive pulmonary disease (COPD) patients in Japan remain undiagnosed, primarily due to the underuse of spirometry. Two studies were conducted to see whether the COPD Assessment Test (CAT) in primary care has the potential to identify those patients who need spirometry for a diagnosis of COPD and to determine whether patients with cardiovascular disease had airflow limitation, which could be detected by CAT. MATERIALS AND METHODS: Two multicenter, noninterventional, prospective studies (studies 1 and 2) were conducted across Japan. Patients in both studies were ≥40 years old with a smoking history. Those in study 1 were seen in primary care and had experienced repeated respiratory tract infections, but had no diagnosis of COPD. Patients in study 2 were identified in cardiovascular disease clinics when routinely visiting for their cardiovascular disease. All patients completed the CAT prior to lung-function testing by hand-held spirometry. The presence of airflow limitation was defined as a forced expiratory volume in 1 second (FEV1)/FEV6 ratio<0.73. RESULTS: A total of 3,062 subjects completed the CAT (2,067 in study 1, 995 in study 2); 88.8% were male, and the mean age (±standard deviation) was 61.5±11.6 years. Airflow limitation was found in 400 (19.4%) patients in study 1, and 269 (27.0%) in study 2. The CAT score in patients with airflow limitation was significantly higher than in patients without airflow limitation in both studies: 8.6 (95% confidence interval [CI] 7.9-9.2) versus 7.4 (95% CI 7.1-7.6) in study 1, and 8.3 (95% CI 7.5-9.2) versus 6.4 (95% CI 6.0-6.8) in study 2 (both P<0.001). CONCLUSION: These findings suggest that the CAT has the potential to identify patients with cardiovascular disease or a history of frequent chest infections who need spirometry to diagnose COPD

Noise Enhanced Stability in Fluctuating Metastable States

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: the average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.Comment: 7 pages, 5 figures, to appear in Phys. Rev. E vol. 69 (6),200

Comparison of postoperative pulmonary function and air leakage between pleural closure vs. mesh-cover for intersegmental plane in segmentectomy

<p>Abstract</p> <p>Background</p> <p>To prevent postoperative air leakage after lung segmentectomy, we used two methods for the intersegmental plane: closing it by suturing the pleural edge (pleural closure), or opening it with coverage using polyglycolic acid mesh and fibrin glue (mesh-cover). The preserved forced expiratory volume in one second (FEV₁) of each lobe and the postoperative air leakage were compared between the two groups.</p> <p>Methods</p> <p>For 61 patients who underwent pleural closure and 36 patients who underwent mesh-cover, FEV₁of the lobe before and after segmentectomy was measured using lung-perfusion single-photon-emission computed tomography and CT (SPECT/CT). The groups' results were compared, revealing differences of the preserved FEV₁of the lobe for several segmentectomy procedures and postoperative duration of chest tube drainage.</p> <p>Results</p> <p>Although left upper division segmentectomy showed higher preserved FEV₁of the lobe in the mesh-cover group than in the pleural closure one (<it>p </it>= 0.06), the other segmentectomy procedures showed no differences between the groups. The durations of postoperative chest drainage in the two groups (2.0 ± 2.5 vs. 2.3 ± 2.2 days) were not different.</p> <p>Conclusions</p> <p>Mesh-cover preserved the pulmonary function of remaining segments better than the pleural closure method in left upper division segmentectomy, although no superiority was found in the other segmentectomy procedures. However, the data include no results obtained using a stapler, which cuts the segment without recognizing even the intersegmental plane and the intersegmental vein. Mesh-cover prevented postoperative air leakage as well as the pleural closure method did.</p

Combined subsegmentectomy: postoperative pulmonary function compared to multiple segmental resection

<p>Abstract</p> <p>Background</p> <p>For small peripheral c-T1N0M0 non-small cell lung cancers involving multiple segments, we have conducted a resection of subsegments belonging to different segments, i.e. combined subsegmentectomy (CSS), to avoid resection of multiple segments or lobectomy. Tumor size, location of tumor, and forced expiratory volume in 1 second (FEV₁) of each preserved lobe were compared among the CSS, resection of single segment, and that of multiple segments.</p> <p>Methods</p> <p>FEV₁of each preserved lobe were examined in 17 patients who underwent CSS, 56 who underwent resection of single segment, and 41 who underwent resection of multiple segments, by measuring pulmonary function and lung-perfusion single-photon-emission computed tomography and computed tomography before and after surgery.</p> <p>Results</p> <p>Tumor size in the CSS was significantly smaller than that in the resection of multiple segments (1.4 ± 0.5 vs. 2.0 ± 0.8 cm, p = 0.002). Tumors in the CSS were located in the right upper lobe more frequently than those in the resection of multiple segments (53% vs. 5%, p < 0.001). Postoperative of FEV₁of each lobe after the CSS was higher than that after the resection of multiple segments (0.3 ± 0.2 vs. 0.2 ± 0.2 l, p = 0.07). Mean FEV₁of each preserved lobe per subsegment after CSS was significantly higher than that after resection of multiple segments (0.05 ± 0.03 vs. 0.03 ± 0.02 l, p = 0.02). There was no significant difference of these factors between the CSS and resection of single segment.</p> <p>Conclusions</p> <p>The CSS is effective for preserving pulmonary function of each lobe, especially for small sized lung cancer involving multiple segments in the right upper lobe, which has fewer segments than other lobes.</p

λ-backbone colorings along pairwise disjoint stars and matchings

Given an integer λ≥2, a graph G=(V,E) and a spanning subgraph H of G (the backbone of G), a λ-backbone coloring of (G,H) is a proper vertex coloring V→{1,2,…} of G, in which the colors assigned to adjacent vertices in H differ by at least λ. We study the case where the backbone is either a collection of pairwise disjoint stars or a matching. We show that for a star backbone S of G the minimum number ℓ for which a λ-backbone coloring of (G,S) with colors in {1,…,ℓ} exists can roughly differ by a multiplicative factor of at most View the MathML source from the chromatic number χ(G). For the special case of matching backbones this factor is roughly View the MathML source. We also show that the computational complexity of the problem “Given a graph G with a star backbone S, and an integer ℓ, is there a λ-backbone coloring of (G,S) with colors in {1,…,ℓ}?” jumps from polynomially solvable to NP-complete between ℓ=λ+1 and ℓ=λ+2 (the case ℓ=λ+2 is even NP-complete for matchings). We finish the paper by discussing some open problems regarding planar graphs