First time here? Checkout the FAQ!
0 votes
Let G be a planar graph such that every face is bordered by exactly 3 edges.Which of the following can never be the value for χ(G) ? (where χ(G) is the chromatic number of G)

a)  2

b)  3

c)  4

d)  None of these

PS : (Explain: "every face is bordered by exactly 3 edges. ")
asked in Graph Theory by Loyal (3.1k points)  
edited by | 86 views

2 Answers

+1 vote

I think answer should be (A) because K2 require 2 colors and is not bounded by three edges but Krequire 3 colors, and K4 require 4 colors to color them and both of them are planar graphs and are bounded by exactly 3 edges. Moreover, every face is bordered by exactly three edges means that every REGION formed within the graph must have exactly three edges surrounding them. Have a look at the graphs, every region within graph K3 and K4 are bounded by exactly three edges but K2 is not.

answered by Active (1.5k points)  
edited by
0 votes
as it mentions it's planar and every face is bounded by exactly three edges so the only possibility we have K3 which has chromatic number X(G) =3
answered by Boss (5.4k points)  

Related questions

Top Users Apr 2017
  1. akash.dinkar12

    3508 Points

  2. Divya Bharti

    2542 Points

  3. Deepthi_ts

    2040 Points

  4. rude

    1966 Points

  5. Tesla!

    1768 Points

  6. Shubham Sharma 2

    1610 Points

  7. Debashish Deka

    1588 Points

  8. Arunav Khare

    1454 Points

  9. Kapil

    1424 Points

  10. Arjun

    1420 Points

Monthly Topper: Rs. 500 gift card

22,075 questions
28,041 answers
24,135 users