We combine the concepts of list colorings of graphs with the concept of defective colorings of graphs and introduce the concept of defective list colorings. We apply these concepts to vertexâ€¦ (More)

Given a connected graph G, and a distribution of t pebbles to the vertices of G, a pebbling step consists of removing two pebbles from a vertex v and placing one pebble on a neighbor of v. For aâ€¦ (More)

Let G1 and G2 be two graphs on n vertices with 2(G1)=d1 and 2(G2)=d2 . A packing of G1 and G2 is a set L=[H1 , H2] such that H1 $G1 , H2 $G2 , and H1 and H2 are edge disjoint subgraphs of Kn . B.â€¦ (More)

Two variations of set intersection representation are investigated and upper and lower bounds on the minimum number of labels with which a graph may be represented are found that hold for almost allâ€¦ (More)

For a graph G = (V, E) and integer p, a p-intersection representation is a family = {Sx: x E V} of subsets of a set S with the property that IS, n S,l 2 p {u, u } E E. It is conjectured in 111 thatâ€¦ (More)

When G is a graph with average degree greater than k âˆ’ 2, ErdÅ‘s and Gallai proved that G contains a path on k vertices. ErdÅ‘s and SÃ³s conjectured that under the same condition, G should contain everyâ€¦ (More)