42366271
A Note on the m-Bounded Chromatic Number of a Tree
Abstract The m-bounded chromatic number of a graph G is the smallest number of colors required for a proper coloring of G in which each color is used at most m times. We will establish an exact formula for the m -bounded chromatic number of a tree.
12831347
Equitable Coloring and the Maximum Degree
Abstract Let Δ(G) denote the maximum degree of a graph G . The equitable Δ-coloring conjecture asserts that a connected graph G is equitably Δ( G )-colorable if it is different from K m , C 2 m + 1 and K 2 m + 1,2 m + 1 for all m ⩾ 1. This conjecture is established for graphs G satisfying Δ( G ) ⩾ | G |/2 or Δ( G ) ⩽ 3.
38200007
Total colorings of equibipartite graphs
Abstract The total chromatic number χτ ( G ) of a graph G is the least number of colors needed to color the vertices and the edges of G such that no adjacent or incident pair of elements receive the same color. A simple graph G is called type 1 if χτ ( G ) = Δ ( G ) + 1, where Δ ( G ) is the maximum degree of G . In this paper we prove the following conjecture of Chen et al.: An ( n − 2)-regular equibipartite graph K n , n − E ( J ) is type 1 if and only if J contains a 4-cycle.
16547141
Edge domination in complete partite graphs
Abstract An edge dominating set in a graph G is a set of edges D such that every edge not in D is adjacent to an edge of D . An edge domatic partition of a graph G =( V , E ) is a collection of pairwise-disjoint edge dominating sets of G whose union is E . The maximum size of an edge domatic partition of G is called the edge domatic number . In this paper, we study the edge domatic number of the complete partite graphs and give the answers for balanced complete partite graphs and complete split graphs .
16166391
Linear k-arboricities on trees
Abstract For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number l such that the edge set E(G) can be partitioned into l disjoint sets and that each induces a subgraph whose components are paths of lengths at most k. This paper studies linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm to determine whether a tree T has lak(T)⩽m.
6763688
Paint Inspired Color Mixing and Compositing for Visualization
Color is often used to convey information, and color compositing is often required while visualizing multiattribute information. This paper proposes an alternative method for color compositing. In order to present understandable color blending to the general public, several techniques are proposed. First, a paint-inspired RYB color space is used. In addition, noise patterns are employed to produce subregions of pure color within an overlapped region. We show examples to demonstrate the effectiveness of our technique for visualization
13073706
Graph homotopy and Graham homotopy
Abstract Simple-homotopy for cell complexes is a special type of topological homotopy constructed by elementary collapses and elementary expansions. In this paper, we introduce graph homotopy for graphs and Graham homotopy for hypergraphs and study the relation between the two homotopies and the simple-homotopy for cell complexes. The graph homotopy is useful to describe topological properties of discretized geometric figures, while the Graham homotopy is essential to characterize acyclic hypergraphs and acyclic relational database schemes.
694380
Automatic Fault Tree Derivation from Little-JIL Process Definitions
Defects in safety critical processes can lead to accidents that result in harm to people or damage to property. Therefore, it is important to find ways to detect and remove defects from such processes. Earlier work has shown that Fault Tree Analysis (FTA) [3] can be effective in detecting safety critical process defects. Unfortunately, it is difficult to build a comprehensive set of Fault Trees for a complex process, especially if this process is not completely well-defined. The Little-JIL process definition language has been shown to be effective for defining complex processes clearly and precisely at whatever level of granularity is desired [1]. In this work, we present an algorithm for generating Fault Trees from Little-JIL process definitions. We demonstrate the value of this work by showing how FTA can identify safety defects in the process from which the Fault Trees were automatically derived.
17041567
On-line scheduling of small open shops
We investigate the problem of on-line scheduling open shops of two and three machines with an objective of minimizing the schedule makespan. We first propose a 1.848-competitive permutation algorithm for the non-preemptive scheduling problem of two machines and show that no permutation algorithm can be better than 1.754-competitive. Secondly, we develop a (27/19)-competitive algorithm for the preemptive scheduling problem of three machines, which is most competitive.
42742272
Definition and Analysis of Election Processes
This paper shows that process definition and analysis technologies can be used to reason about the vulnerability of election processes with respect to incorrect or fraudulent behaviors by election officials. The Little-JIL language is used to model example election processes, and various election worker fraudulent behaviors. The FLAVERS finite-state verification system is then used to determine whether different combinations of election worker behaviors cause the process to produce incorrect election results or whether protective actions can be used to thwart these threats.