We show that the 4-coloring problem can be solved in polynomial time for graphs with no induced 5-cycle C5 and no induced 6-vertex path P6.

This paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U2, 6 -, U4, 6 -, P6 -, F & 7 -, or (F & 7 )*-minors. Explicitly, these matroids are all minors of S(5, 6, 12) with rank and corank at least 4, and P"8 , the matroid that ca...

Monitoring changes in landscape cover types has been a great concern for forest and wildlife managers. Both managers find it very important to know how much area is suitable for wildlife species and what areas are affected due to anthropogenic pressure. To address these concerns, evaluation of Chandoli National Park was done to see the changes that have taken place over the past 28 years. The N...

Pictures are the most effective means of conveying information. A picture is worth a thousand words. Pictures concisely convey information about positions, sizes and interrelationships between objects. Human beings are good at deriving information from such images, because of our innate visual and mental abilities. About 75% of the information received by human is in pictorial form. The paper d...

We prove that there are 24 4-critical P6-free graphs, and give the complete list. We remark that, if H is connected and not a subgraph of P6, there are infinitely many 4-critical H-free graphs. Our result answers questions of Golovach et al. and Seymour.