[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Swarm robotics is an approach to collective robotics that takes inspiration from the self-organized behaviors of social animals. Through simple rules and local interactions, swarm robotics aims at designing robust, scalable, and flexible collective behaviors for the coordination of large numbers of robots. In this paper, we analyze the literature from the point of view of swarm engineering: we focus mainly on ideas and concepts that contribute to the advancement of swarm robotics as an engineering field and that could be relevant to tackle real-world applications. Swarm engineering is an emerging discipline that aims at defining systematic and well founded procedures for modeling, designing, realizing, verifying, validating, operating, and maintaining a swarm robotics system. We propose two taxonomies: in the first taxonomy, we classify works that deal with design and analysis methods; in the second taxonomy, we classify works according to the collective behavior studied. We conclude with a discussion of the current limits of swarm robotics as an engineering discipline and with suggestions for future research directions.

/pdf/swarm-robotics-a-review-from-the-swarm-engineering-46mfc058e6.pdf

Swarm robotics: a review from the swarm engineering perspective

Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.

/pdf/graph-coloring-problems-4v7vijos3s.pdf

Graph Coloring Problems

: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.

http://www.dtic.mil/dtic/tr/fulltext/u2/a273552.pdf

Discrete Applied Mathematics

Disjoint Spanning Arborescences in k-Arc-Strong Digraphs

Let be a sequence of of nonnegative integers pairs. If a digraph D with satisfies and for each i with , then d is called a degree sequence of D. If D is a strict digraph, then d is called a strict digraphic sequence. Let be the collection of digraphs with degree sequence d. We characterize strict digraphic sequences d for which there exists a strict strong digraph .

Characterization of Digraphic Sequences with Strongly Connected Realizations

Hamiltonian s-properties and eigenvalues of k-connected graphs

Strength and fractional arboricity of complementary graphs

An orientation of a graph $G$ is a mod (2p+1)-orientation if, under this orientation, the net out-degree at every vertex is congruent to zero mod 2p+1. If, for any function $b: V(G) \rightarrow \mathbb Z_{2p+1}$ satisfying $\sum_{v \in V(G)} b(v) \equiv 0$ (mod 2p+1), $G$ always has an orientation $D$ such that the net out-degree at every vertex $v$ is congruent to $b(v)$ mod 2p+1, then $G$ is strongly $\mathbb Z_{2p+1}$-connected. The graph $G'$ obtained from $G$ by contracting all nontrivial subgraphs that are strongly $\mathbb Z_{2s+1}$-connected is called the $\mathbb Z_{2s+1}$-reduction of $G$. Motivated by a minimum degree condition of Barat and Thomassen [J. Graph Theory, 52 (2006), pp. 135--146], and by the Ore conditions of Fan and Zhou [SIAM J. Discrete Math., 22 (2008), pp. 288--294] and of Luo et al. [European J. Combin., 29 (2008), pp. 1587--1595] on $\mathbb Z_3$-connected graphs, we prove that for a simple graph $G$ on $n$ vertices, and for any integers $s > 0$ and real numbers $\alpha, \be...

/pdf/on-mod-2s-1-orientations-of-graphs-2by3k4d41j.pdf

Hong-Jian Lai

Papers

Disjoint Spanning Arborescences in k-Arc-Strong Digraphs

Characterization of Digraphic Sequences with Strongly Connected Realizations

Hamiltonian s-properties and eigenvalues of k-connected graphs

Strength and fractional arboricity of complementary graphs

On Mod $(2s+1)$-Orientations of Graphs