In this paper, we study the enumeration of certain classes of graphs that can be fully characterized by tree decompositions; these classes are particularly significant due to the algorithmic improvements derived from tree decompositions on classically NP-complete problems on these classes [12, 7, 17, 35]. Previously, Chauve et al. [6] and Iriza [26] constructed grammars from the split decomposi...

The ability to express “derived predicates” in the formalization of a planning domain is both practically and theoretically important. The recent PDDL2.2 language supports derived predicates, which can be expressed by “domain rules”. We propose an approach to planning with derived predicates where the search space consists of particular graphs of actions and rules, called rule-action graphs, re...

This paper is a tutorial on the application of graph theoretic techniques in classical coding theory. A fundamental problem in coding theory is to determine the maximum size of a code satisfying a given minimum Hamming distance. This problem is thought to be extremely hard and still not completely solved. In addition to a number of closed form expressions for special cases and some numerical re...

We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, graphs are not translation invariant, do admit any group structure and spatially non-homogeneous. Despite these crucial differences, we compute asymptotics of Martin kernel, deduce boundary show that it is minimal. Similar results grid $\mathbb {Z}^{d}$ derived in a celebrated work Ney Spitzer.

Day and Tripathi [K. Day, A. Tripathi, Unidirectional star graphs, Inform. Process. Lett. 45 (1993) 123–129] proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs. Cheng and Lipman [E. Cheng, M.J. Lipman, On the Day–Tripathi orientation of the star graphs: Connectivity, Inform. Process. Lett. 73 (2000) 5–10; E. Cheng, M.J. Li...

The ability to express “derived predicates” in the formalization of a planning domain is both practically and theoretically important. In this paper, we propose an approach to planning with derived predicates where the search space consists of “Rule-Action Graphs”, particular graphs of actions and rules representing derived predicates. We present some techniques for representing rules and reaso...

solvable graphs (also known as reachable graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). in this paper, the properties of solvable graphs are investigated, and a new concept in multi agent moti...

We propose a random graph model which is a special case of sparse random graphs with given degree sequences which satisfy a power law. This model involves only a small number of parameters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For exam...

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovász and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. ...

We define a signed embedding of a signed graph into real projective space to be an embedding such that an embedded cycle is 0-homologous if and only if it is balanced. We characterize signed graphs that have a linkless signed embedding. In particular, we exhibit 46 graphs that form the complete minor-minimal set of signed graphs that contain a nonsplit link for every signed embedding. With one ...