[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

Motivated by the Chinese Postman Problem, Boesch, Suffel, and Tindell [The spanning subgraphs of Eulerian graphs, J. Graph Theory 1 (1977), pp. 79–84] proposed the supereulerian graph problem which seeks the characterization of graphs with a spanning Eulerian subgraph. Pulleyblank [A note on graphs spanned by Eulerian graphs, J. Graph Theory 3 (1979), pp. 309–310] showed that the supereulerian problem, even within planar graphs, is NP-complete. In this paper, we settle an open problem raised by An and Xiong on characterization of supereulerian graphs with small matching numbers. A well-known theorem by Chvatal and Erdos [A note on Hamilton circuits, Discrete Math. 2 (1972), pp. 111–135] states that if G satisfies α(G)≤κ(G), then G is hamiltonian. Flandrin and Li in 1989 showed that every 3-connected claw-free graph G with α(G)≤2 κ(G) is hamiltonian. Our characterization is also applied to show that every 2-connected claw-free graph G with α(G)≤3 is hamiltonian, with only one well-characterized exceptional...

Supereulerian graphs with small matching number and 2-connected hamiltonian claw-free graphs

Note: On s-hamiltonian-connected line graphs

Minimum degree conditions for the Hamiltonicity of 3-connected claw-free graphs

For an integer s ≥ 0, a graph G is s-hamiltonian if for any ver- tex subset S � ⊆ V (G) with |S � |≤ s, G − Sis hamiltonian. It is well known that if a graph G is s-hamiltonian, then G must be (s + 2)-connected. The converse is not true, as there exist arbitrarily highly connected nonhamil- tonian graphs. But for line graphs, we prove that when s ≥ 5, a line graph is s-hamiltonian if and only if it is (s + 2)-connected. C

On s-Hamiltonian Line Graphs

In a partial inverse combinatorial problem, given a partial solution, the goal is to modify data as small as possible such that there exists an optimal solution containing the given partial solution. In this paper, we study a constraint version of the partial inverse matroid problem in which the weight can only be increased. Two polynomial time algorithms are presented for this problem.

Hong-Jian Lai

Papers

Supereulerian graphs with small matching number and 2-connected hamiltonian claw-free graphs

Note: On s-hamiltonian-connected line graphs

Minimum degree conditions for the Hamiltonicity of 3-connected claw-free graphs

On s-Hamiltonian Line Graphs

Algorithms for the partial inverse matroid problem in which weights can only be increased