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BigPicture is a project management and portfolio management app for Jira environment. First released in 2014 and developed by SoftwarePlant (now by AppFire), it delivers tools for project managers that the core Jira lacks, i.e. roadmap, a Gantt chart, Scope (work breakdown structure), risks, resources and teams modules.
A list edge-coloring is a choice of a color for each edge, from its list of allowed colors; a coloring is proper if no two adjacent edges receive the same color. A graph G is k-edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has
Jira (/ ˈ dʒ iː r ə / JEE-rə) [4] is a software product developed by Atlassian that allows bug tracking, issue tracking and agile project management.Jira is used by a large number of clients and users globally for project, time, requirements, task, bug, change, code, test, release, sprint management.
The road coloring problem is the problem of edge-coloring a directed graph with uniform out-degrees, in such a way that the resulting automaton has a synchronizing word. Trahtman (2009) solved the road coloring problem by proving that such a coloring can be found whenever the given graph is strongly connected and aperiodic.
The problem of edge coloring has also been studied in the distributed model. Panconesi & Rizzi (2001) achieve a (2Δ − 1)-coloring in O(Δ + log * n) time in this model. The lower bound for distributed vertex coloring due to Linial (1992) applies to the distributed edge coloring problem as well.
For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.
In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but ...
It is named after Michael O. Albertson, a professor at Smith College, who stated it as a conjecture in 2007; [1] it is one of his many conjectures in graph coloring theory. [2] The conjecture states that, among all graphs requiring n {\displaystyle n} colors, the complete graph K n {\displaystyle K_{n}} is the one with the smallest crossing number.