Minimal elimination ordering for graphs of bounded degree

Minimal elimination ordering for graphs of bounded degree

We show that for graphs of bounded degree, a subset minimal elimination ordering can be determined in almost linear time.

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

Sparse universal graphs for bounded-degree graphs

Let H be a family of graphs. A graph T is H-universal if it contains a copy of each H ∈ H as a subgraph. Let H(k, n) denote the family of graphs on n vertices with maximum degree at most k. For all positive integers k and n, we construct an H(k, n)-universal graph T with Ok(n 2 k log 4 k n) edges and exactly n vertices. The number of edges is almost as small as possible, as Ω(n2−2/k) is a lower...

Spanners of bounded degree graphs

Matching for Graphs of Bounded Degree

We show that there exists a matching with 4m 5k+3 edges in a graph of degree k and m edges.