3-Factor-criticality in double domination edge critical graphs

A vertex subset $S$ of a graph $G$ is a double dominating set of $G$ if $|N[v]\cap S|\geq 2$ for each vertex $v$ of $G$, where $N[v]$ is the set of the vertex $v$ and vertices adjacent to $v$. The double domination number of $G$, denoted by $\gamma_{\times 2}(G)$, is the cardinality of a smallest double dominating set of $G$. A graph $G$ is said to be double domination edge critical if $\gamma_{\times 2}(G+e)<\gamma_{\times 2}(G)$ for any edge $e \notin E$. A double domination edge critical graph $G$ with $\gamma_{\times 2}(G)=k$ is called $k$-$\gamma_{\times 2}(G)$-critical. A graph $G$ is $r$-factor-critical if $G-S$ has a perfect matching for each set $S$ of $r$ vertices in $G$. In this paper we show that $G$ is 3-factor-critical if $G$ is a 3-connected claw-free $4$-$\gamma_{\times 2}(G)$-critical graph of odd order with minimum degree at least 4 except a family of graphs.Comment: 14 page

On characterization of uniquely 3-list colorable complete multipartite graphs

For each vertex v of a graph G, if there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. Ghebleh and Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for nine graphs: $K_{2,2,r}$ r ∈ {4,5,6,7,8}, $K_{2,3,4}$, $K_{1*4,4}$, $K_{1*4,5}$, $K_{1*5,4}$. Also, they conjectured that the nine graphs are not U3LC graphs. After that, except for $K_{2,2,r}$ r ∈ {4,5,6,7,8}, the others have been proved not to be U3LC graphs. In this paper we first prove that $K_{2,2,8}$ is not U3LC graph, and thus as a direct corollary, $K_{2,2,r}$ (r = 4,5,6,7,8) are not U3LC graphs, and then the uniquely 3-list colorable complete multipartite graphs are characterized completely

The Complexity of Secure Domination Problem in Graphs

A dominating set of a graph G is a subset D ⊆ V (G) such that every vertex not in D is adjacent to at least one vertex in D. A dominating set S of G is called a secure dominating set if each vertex u ∈ V (G) \ S has one neighbor v in S such that (S \ {v}) ∪ {u} is a dominating set of G. The secure domination problem is to determine a minimum secure dominating set of G. In this paper, we first show that the decision version of the secure domination problem is NP-complete for star convex bipartite graphs and doubly chordal graphs. We also prove that the secure domination problem cannot be approximated within a factor of (1−ε) ln |V | for any ε > 0, unless NP⊆DTIME (|V |O(log log |V|)). Finally, we show that the secure domination problem is APX-complete for bounded degree graphs

Total kk-distance domination critical graphs

A set $S$ of vertices in a graph $G=(V,E)$ is called a total$k$-distance dominating set if every vertex in $V$ is withindistance $k$ of a vertex in $S$. A graph $G$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (G - x) < gamma_{t}^{k}(G)$ for any vertex $xin V(G)$. In this paper,we investigate some results on total $k$-distance domination-critical of graphs

Major inducing factors of hypertensive complications and the interventions required to reduce their prevalence: an epidemiological study of hypertension in a rural population in China

Abstract Background The complications of hypertension cause severe health problems in rural areas in China. We (i) screened the major factors inducing hypertensive complications and provided intervention measures; and (ii) verified the efficacy of the New Rural Cooperative Medical Scheme (NRCMS; a medical insurance scheme for rural residents) for hypertension management. Methods A survey was conducted in the villages of Yunnan (an underdeveloped province in southwest China). The NRCMS was initiated there in 2005. Data were collected through questionnaires, physical examination, electrocardiography, as well as blood and urine tests. To detect factors inducing hypertension complications, a generalized estimating equations model was developed. Multivariable logistic regression was used to analyze influencing factors for hypertension control. Results Poor management of hypertension was observed in women. Being female, old, poorly educated, a smoker, ignorant of the dangerousness of hypertension, and having uncontrolled hypertension made patients more prone to hypertension complications. Combination therapy with ≥2 drugs helped control hypertension, but most rural patients disliked multidrug therapy because they considered it to be expensive and inconvenient. The NRCMS contributed little to reduce the prevalence of complications and improve control of hypertension. Conclusions The present study suggested that the NRCMS needs to be reformed to concentrate on early intervention in hypertension and to concentrate on women. To increase hypertension control in rural areas in China, compound products containing effective and inexpensive drugs (and not multidrug therapy) are needed.</p

Comparison of Transperitoneal and Retroperitoneal Robotic Partial Nephrectomy for Patients with Completely Lower Pole Renal Tumors

(1) Background: For completely lower pole renal tumors, we compared the perioperative outcomes of robotic partial nephrectomy via transperitoneal and retroperitoneal approaches. (2) Methods: Complete lower pole renal tumors were defined as tumors that received 1 point for the “L” element of the R.E.N.A.L. and located at the lower pole of kidney. After confirming consistency in baseline characteristics, oncological and functional benefits were compared. Pentafecta achievement was used to represent the perioperative optimal outcome, followed by multivariate analysis of factors associated with the lack of pentafecta achievement. (3) Results: Among 151 patients identified, 116 (77%) underwent robotic partial nephrectomy via a transperitoneal approach and 35 (23%) via a retroperitoneal approach. Patients undergoing transperitoneal robotic partial nephrectomy experienced more blood loss than those undergoing retroperitoneal robotic partial nephrectomy (50 mL vs. 40 mL, p = 0.015). No significant differences were identified for operative time (120 min vs. 120 min), ischemia time (19 min vs. 20 min), positive surgical margins (0.0% vs. 2.86%), postoperative rate of complication (12.07% vs. 5.71%). No significant differences were identified in pathologic variables, eGFR decline in postoperative 12-month (3.9% vs. 5.4%) functional follow-up. Multivariate cox analysis showed that tumor size (OR: 0.523; 95% CI: 0.371–0.736; p < 0.001) alone was independently correlated to the achievement of pentafecta. (4) Conclusions: For completely lower pole renal tumors, transperitoneal and retroperitoneal robotic partial nephrectomy provide similar outcomes. These two surgical approaches remain feasible options for these cases