# chromatic number of a graph

Chicago, IL: University In general, the graph Mi is triangle-free, (i −1)- vertex-connected, and i - chromatic. Take a look at vertex B. As I mentioned above, we need to know the chromatic polynomial first. She has 15 years of experience teaching collegiate mathematics at various institutions. number of equals the largest number of pairwise https://www.ics.uci.edu/~eppstein/junkyard/plane-color.html. to bound the chromatic number of random lifts of graphs; this parameter’s relation to the chromatic number is also discussed in . Services. Did you know… We have over 220 college The wiki page linked to in the previous paragraph has some algorithms descriptions which you can probably use. 8, 9, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, ... (OEIS A000934). Although it is "well known" that a (simple) series parallel graph has chromatic number at most 3, I cannot seem to find a proof of this statement anywhere. a connection directly back to itself) could never be properly colored, it is understood that graphs in this context are loopless. Theorem: If G has maximum degree ∆, then G is (∆ +1)–colorable. Log in or sign up to add this lesson to a Custom Course. courses that prepare you to earn However, it can become quite difficult to find the chromatic number in more involved graphs. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Heawood conjecture. It is NP-Complete even to determine if a given graph is 3-colorable (and also to find a coloring). Skiena 1990, p. 215). graph." The chromatic number of a graph is the minimal number of colors for which a graph coloring is possible. The algorithm can produce all the optimal independent ways of colouring the graph. Earn Transferable Credit & Get your Degree, Bipartite Graph: Definition, Applications & Examples, Euler's Theorems: Circuit, Path & Sum of Degrees, Graphs in Discrete Math: Definition, Types & Uses, The Traveling Salesman Problem in Computation, Fleury's Algorithm for Finding an Euler Circuit, Mathematical Models of Euler's Circuits & Euler's Paths, Weighted Graphs: Implementation & Dijkstra Algorithm, Multinomial Coefficients: Definition & Example, Difference Between Asymmetric & Antisymmetric Relation, Page Replacement: Definition & Algorithms, Associative Memory in Computer Architecture, Thread State Diagrams, Scheduling & Switches, Dijkstra's Algorithm: Definition, Applications & Examples, SAT Subject Test Mathematics Level 1: Practice and Study Guide, SAT Subject Test Mathematics Level 2: Practice and Study Guide, Holt McDougal Algebra 2: Online Textbook Help, McDougal Littell Pre-Algebra: Online Textbook Help, GACE Mathematics (522): Practice & Study Guide, Ohio Assessments for Educators - Mathematics (027): Practice & Study Guide, Common Core Math Grade 7 - Expressions & Equations: Standards, CUNY Assessment Test in Math: Practice & Study Guide, ILTS Mathematics (208): Test Practice and Study Guide, Prentice Hall Algebra 2: Online Textbook Help, Smarter Balanced Assessments - Math Grade 7: Test Prep & Practice, Common Core Math - Geometry: High School Standards, Common Core Math - Functions: High School Standards, Common Core Math Grade 8 - Expressions & Equations: Standards. credit-by-exam regardless of age or education level. Introduction 2. For a fixed probabilityp, 0