The existence of a connected 12-regular {K4, K2,2,2}-ultrahomogeneous graph G is established, (i.e. each isomorphism between two copies of K4 or K2,2,2 in G extends to an automorphism of G), with the 42 ordered lines of the Fano plane taken as vertices. This graph G can be expressed in a unique way both as the edge-disjoint union of 42 induced copies of K4 and as the edge-disjoint union of 21 i...

In this paper, we design the first polynomial time approximation scheme for d-hop connected dominating set (d-CDS) problem in growth-bounded graphs, which is a general type of graphs including unit disk graph, unit ball graph, etc. Such graphs can represent majority types of existing wireless networks. Our algorithm does not need geometric representation (e.g., specifying the positions of each ...

Fifty years ago Erdős asked to determine the minimum number of k-cliques in a graph on n vertices with independence number less than l. He conjectured that this minimum is achieved by the disjoint union of l− 1 complete graphs of size n l−1 . This conjecture was disproved by Nikiforov who showed that the balanced blow-up of a 5-cycle has fewer 4-cliques than the union of 2 complete graphs of si...

For a graph property P and a graph G , a subset S of vertices of G is a P -set if the subgraph induced by S has the property P . The domination number with respect to the property P , denoted by γP(G) , is the minimum cardinality of a dominating P -set. Any property P satisfied by all edgeless graphs is called nondegenerate. For any graph G with n vertices and maximum degree ∆(G) , γP(G) ≤ n−∆(...

List coloring generalizes graph coloring by requiring the color of a vertex to be selected from a list of colors specific to that vertex. One refinement of list coloring, called choosability with separation, requires that the intersection of adjacent lists is sufficiently small. We introduce a new refinement, called choosability with union separation, where we require that the union of adjacent...

An antimatroid is an accessible union-closed family of subsets of a 0nite set. A number of classes of antimatroids are closed under taking minors such as point-search antimatroids of rooted (di)graphs, line-search antimatroids of rooted (di)graphs, shelling antimatroids of rooted trees, shelling antimatroids of posets, etc. The forbidden minor characterizations are known for point-search antima...

A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex of G sees all k colors on its closed neighborhood. We denote Fall(G) the set of all positive integers k for which G has a fall k-coloring. In this paper, we study fall colorings of lexicographic product of graphs and categorical product of graphs and answer a question of [3] about fall colorings of categorical prod...

 Abstract  Background: Reamed interlocking intramedullary nailing of the tibia is a procedure  for the treatment of a non-infected tibial non:::union:::. The purpose of this clinical  study was to evaluate the outcome of this method as a treatment of tibial non:::union:::.  Methods: Twenty-nine patients with non:::union::: after initial therapy for tibial fracture  were retrospectively assessed...

Multiply sectioned Bayesian networks (MSBNs) provides a coherent framework for probabilistic inference in a cooperative multiagent distributed interpretation system. Inference in MSBNs can be performed e ectively using a compiled representation. The compilation involves the triangulation of the collective dependency structure (a graph) de ned in terms of the union of a set of local dependency s...

Treewidth and branchwidth are two closely related connectivity parameters of graphs. Graphs of treewidth at most k have well-known alternative characterizations as subgraphs of chordal graphs and as partial k-trees. In this paper we give analogous alternative characterizations for graphs of branchwidth at most k. We first show that they are the subgraphs of chordal graphs where every maximal cl...