Let $G$ be a connected graph with the usual shortest-path metric $d$. The is $\delta$-hyperbolic provided for any vertices $x,y,u,v$ in it, two larger of three sums $d(u,v)+d(x,y),d(u,x)+d(v,y)$ and $d(u,y)+d(v,x)$ differ by at most $2\delta.$ $k$-chordal it has no induced cycle length greater than $k.$ Brinkmann, Koolen Moulton find that every $3$-chordal $1$-hyperbolic not $\frac{1}{2}$-hyperbolic if only contains one special graphs as an isometric subgraph. For $k\geq 4,$ we show must...

We construct multisoliton solutions for the $L^2$-critical Hartree equation with trajectories asymptotically obeying a many-body law an inverse square potential. Precisely, we consider $m$-body hyperbolic and parabolic non-trapped dynamics. The pseudo-conformal symmetry then implies finite-time collision blow up in latter case solution blowing at $m$ distinct points former case. approach take is based on ideas of [Krieger-Martel-Rapha\"el, 2009] third author's recent extension. approximation...

The purpose of this study was to investigate the efficacy magnetic resonance imaging (MRI) radiomics in differentiating hepatocellular carcinoma (HCC) from intrahepatic cholangiocarcinoma (ICC). clinical and MRI data 129 pathologically confirmed HCC patients 48 ICC treated at Affiliated Hospital North Sichuan Medical College between April 2016 December 2021 were retrospectively analyzed. randomly divided a ratio 7:3 into training group 124 (90 with 34 ICC) validation 53 (39 14 ICC). Radiomic...

Let $G$ be a connected graph with the usual shortest-path metric $d$. The is $δ$-hyperbolic provided for any vertices $x,y,u,v$ in it, two larger of three sums $d(u,v)+d(x,y),d(u,x)+d(v,y)$ and $d(u,y)+d(v,x)$ differ by at most $2δ.$ $k$-chordal it has no induced cycle length greater than $k.$ Brinkmann, Koolen Moulton find that every 3-chordal 1-hyperbolic not 1/2-hyperbolic if only contains one special graphs as an isometric subgraph. For $k\geq 4,$ we show must $\frac{\lfloor...

Let $G$ be an interval graph and take one of its vertices $x$. Can we find in linear time a minimum number vertex disjoint paths which cover the set have $x$ as their endpoints? This paper provides positive answer to this problem. In course developing such algorithm, explore possibility getting insight on path structure graphs via greedy searches.

Graph Theory In their 2009 paper, Corneil et al. design a linear time interval graph recognition algorithm based on six sweeps of Lexicographic Breadth-First Search (LBFS) and prove its correctness. They believe that corresponding 5-sweep LBFS is also correct. Thanks to the structure theory established mainly by al., we are able present 4-sweep which determines whether or not input unit an graph. Like our does involve any complicated data can be executed in time.

A spanning connectedness property is one which involves the robust existence of a subgraph some special form, say Hamiltonian cycle in sequence vertices appear an arbitrarily given ordering, or path obtained by deleting any three vertices, internally-vertex-disjoint paths with endpoints such that meet every vertex graph and cover edges almost linear forest certain fixed size. Let π = π1 · πn be ordering n-vertex G. For positive integer k ≤ n − 1, we call k-thick G provided it holds for all i...

Graphs and Algorithms In this paper we discuss the bounds of relations among various kinds intersection numbers graphs. Especially, address extremal graphs with respect to established bounds. The uniqueness minimum-size representations for some is also studied. course work, introduce a superclass chordal graphs, defined in terms generalization simplicial vertex perfect elimination ordering.

Consider a social network where each person holds an opinion represented by numerical value.Whenever member of the is given chance, updates his/her according to certain convex combination opinions all members.The influence digraph has members as vertices, and there arc from vertex v u if only if, in update formula for v, coefficient u's positive.The sink vertices correspond those stubborn people who never change their opinions.Assuming one sequence, this note provides description resulting...

Let $\mathcal F$ be a set of $k$ by nonnegative matrices such that every "long" product elements is positive. Cohen and Sellers (1982) proved that, then, length $2^k-2$ over must They suggested to investigate the minimum size for which there exists non-positive $2^k-3$ they constructed one example $2^k-2$. We construct further discuss relevant basic problems in framework Boolean linear dynamical systems. also formulate several primitivity properties general discrete