We present a polynomial time algorithm to compute a minimum (weight) feedback vertex set for AT-free graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.

In a finite undirected graph G = (V,E), a vertex v ∈ V dominates itself and its neighbors. A vertex set D ⊆ V in G is an efficient dominating set (e.d. for short) of G if every vertex of G is dominated by exactly one vertex of D. The Efficient Domination (ED) problem, which asks for the existence of an e.d. in G, is known to be NP-complete for P7-free graphs but solvable in polynomial time for ...

This thesis studies the problem of designing efficient algorithms for listing combinatorial structures. The main notion of efficiency that we use is due to Johnson, Yannakakis, and Papadimitriou. It is called polynomial delay. A listing algorithm is said to have delay d if and only if it satisfies the following conditions whenever it is run with any input p: It executes at most d(p) machine ins...

We prove a quantitative, finitary version of Trofimov’s result that connected, locally finite vertex-transitive graph Γ polynomial growth admits quotient with fibres on which the action Aut(Γ) is virtually nilpotent vertex stabilisers. also present some applications. show finite, connected large diameter small abelian stabilisers bounded size. has moderate in sense Diaconis and Saloff-Coste, kn...

In this paper, we introduce a novel graph polynomial called the 'information polynomial' of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform ...

let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values for the vertex-deleted subgraphs of the same graph. This note discusses the polynomial reconstructibility of the matching polynomial. We collect previous resul...

The problem of illuminating a simple n-gon with cn, c < 1 πlights is open, whereas a lower bound of ⌊ 3 5 n⌋ is known. We provide an algorithm for placing π-lights, and experimental results that support the conjecture that ⌊ 3 5 n⌋ lights are also sufficient. We also prove that ⌊ 5 6 n⌋ π-lights suffice if some may be outward facing.