We show that one can compute the injective chromatic number of a chordal graph G at least as efficiently as one can compute the chromatic number of (G−B), where B are the bridges of G. In particular, it follows that for strongly chordal graphs and so-called power chordal graphs the injective chromatic number can be determined in polynomial time. Moreover, for chordal graphs in general, we show ...

The quadratic embedding constant (QE constant) of a graph is new characteristic value defined through the distance matrix. We derive formulae for QE constants join two regular graphs, double graphs and certain lexicographic product graphs. Examples include complete bipartite wheel friendship completely split graph, some associated to strongly

Hadwiger’s conjecture states that for every graph G, χ(G) ≤ η(G), where χ(G) is the chromatic number and η(G) is the size of the largest clique minor in G. In this work, we show that to prove Hadwiger’s conjecture in general, it is sufficient to prove Hadwiger’s conjecture for the class of graphs F defined as follows: F is the set of all graphs that can be expressed as the square graph of a spl...

The problems Contractibility and Induced Minor are to test whether a graph G contains a graph H as a contraction or as an induced minor, respectively. We show that these two problems can be solved in |VG|H |) time if G is a chordal input graph and H is a split graph or a tree. In contrast, we show that containment relations extending Subgraph Isomorphism can be solved in linear time if G is a c...

In this paper, we propose a maximum a posteriori formulation to the multiple target tracking problem. We adopt a graph representation for storing the detected regions as well as their association over time. The multiple target tracking problem is formulated as a multiple paths search in the graph. Due to the noisy foreground segmentation, an object may be represented by several foreground regio...

In this paper, we study the dualization in distributive lattices, a generalization of well-known hypergraph problem. We particular propose equivalent formulations problem terms graphs, hypergraphs, and posets. It is known that amounts to generate all minimal transversals hypergraph, or dominating sets graph. new framework, poset on vertices given together with input (hyper)graph, “ideal solutio...

Directed Acyclic Graphs are often used to model circuits and networks. The path length in such Directed Acyclic Graphs represents circuit or network delays. In the vertex splitting problem, the objective is to determine a minimum number of vertices from the graph to split such that the resulting graph has no path of length greater than a given δ. The problem has been proven to be NP-hard. A Gen...