[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

There have been researches on sufficient spectral conditions for Hamiltonian properties and path-coverable properties of graphs. Utilizing the Bondy-Chv\'atal closure, we provide a unified approach to study sufficient graph eigenvalue conditions for these properties and sharpen former spectral results in [{\em Linear Algebra Appl.}, 432 (2010), 566-570], [{\em Linear Algebra Appl.}, 432 (2010), 2170-2173], [{\em Appl. Mech. Mater.}, 336-338 (2013), 2329-2334], [{\em Linear Algebra Appl.}, 467 (2015), 254-266], [{\em Linear Multilinear Algebra}, 64 (2016), 2252-2269], and [{\em J. Comb. Optim.}, 35 (2018), 1104-1127], among others.

Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

Abelian group colorings were first introduced by Jaeger et al. in [J. Combin. Theory Ser. B, 56 (1992), pp. 165--182] as the dual concept of group connectivity of graphs. For given groups $\Gamma_1...

Hong-Jian Lai

Papers

Unified spectral hamiltonian results of balanced bipartite graphs and complementary graphs

A Note on Group Colorings and Group Structure

The Extremal Sizes of Arc-Maximal (k, l)-Digraphs

Strengthened Ore conditions for (s, t)-supereulerian graphs

Modulo orientations and matchings in graphs