Survey on Intersection of two Maximum Length Paths in Connected Graph

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Survey on Intersection of two Maximum Length Paths in Connected Graph

Author Affiliations

¹Shri Neelkanthaeshwar Govt. Post Graduation College, Khandwa, MP, INDIA
²Department of Mathematics, Indore Institute of Science and Technology, Indore, MP, INDIA

Res. J. Mathematical & Statistical Sci., Volume 2, Issue (3), Pages 1-3, March,12 (2014)

Abstract

In the last decade important results on intersection of two maximum length paths in connected graph were discovered. The aim of this paper is to discuss in detail the progress on the problems of intersecting two maximum length paths, providing some new result in the process. Furthermore we establish the results concerning the intersection of two maximum length paths in 2-connected graph and 3-connected graph

References

Zamfirescu T., Intersecting Longest Paths or Cycles: AShort Survey, An. Univ. Crainova Ser.Mat. Inform., 28,1-9 (2001)
Google Scholar
Axenovich Maria, When do Three Longest Paths have aCommon Vertex?, Discrete Math., Alg. and Appl., 1(1),115-120 (2009)
Google Scholar
De Rezende Susanna F., Fernandes Cristina G., MartinDaniel M. and Wakabayashi Yoshika, Intersection ofLongest Paths in a Graph, Electronic Notes in DiscreteMathematics, 38, 743-748 (2011)
Google Scholar
Skupien Z., Smallest Sets of Longest Paths with EmptyIntersection, Combin. Probab. Comput, 5(4), 429-436(1996)
Google Scholar
Balister P., Györi E., Lehel J. and Schelp R., LongestPaths in Circular Arc Graphs, Combin. Probab. Comput,(13), 311-317 (2004)
Google Scholar
Klavar S. and Petkov?ek M., Graphs with NonemptyIntersection of Longest Paths, Ars Combin, (29), 43-52(1990)
Google Scholar
Paulusma Deniel and Yoshimoto Kiyoshi, RelativeLength of Longest Paths and Cycles in Triangle freeGraphs, Discrete Mathematics, 308(7), 1222-1229 (2008)
Google Scholar
Rautenbach Dieter and Sebastien Sereni Jean, Transversals of Longest Paths and Longest Cycles, CoRRabs, 1302-5503 (2013)
Google Scholar
de Rezende Susanna F., Fernandes Cristina G., MartinDaniel M. and Wakabayashi Yoshika, IntersectingLongest Paths, Discrete Mathematics, 313, 1401-1408(2013)
Google Scholar
Hippchen Thomas, , Intersections of Longest paths andLongest Cycles, Mathematical thesis, Georgia StateUniversity (2008)
Attri Rajesh, Dev Nikhil and Sharma Vivek, Graphtheoretic approach(GTA)- A Multi Attribute DecisionMaking(MADM) Technique, Research Journal Engg, Science, 2(1), 50-53 (2013)
Google Scholar

[ref1] Zamfirescu T., Intersecting Longest Paths or Cycles: AShort Survey, An. Univ. Crainova Ser.Mat. Inform., 28,1-9 (2001)
Google Scholar

[ref2] Axenovich Maria, When do Three Longest Paths have aCommon Vertex?, Discrete Math., Alg. and Appl., 1(1),115-120 (2009)
Google Scholar

[ref3] De Rezende Susanna F., Fernandes Cristina G., MartinDaniel M. and Wakabayashi Yoshika, Intersection ofLongest Paths in a Graph, Electronic Notes in DiscreteMathematics, 38, 743-748 (2011)
Google Scholar

[ref4] Skupien Z., Smallest Sets of Longest Paths with EmptyIntersection, Combin. Probab. Comput, 5(4), 429-436(1996)
Google Scholar

[ref5] Balister P., Györi E., Lehel J. and Schelp R., LongestPaths in Circular Arc Graphs, Combin. Probab. Comput,(13), 311-317 (2004)
Google Scholar

[ref6] Klavar S. and Petkov?ek M., Graphs with NonemptyIntersection of Longest Paths, Ars Combin, (29), 43-52(1990)
Google Scholar

[ref7] Paulusma Deniel and Yoshimoto Kiyoshi, RelativeLength of Longest Paths and Cycles in Triangle freeGraphs, Discrete Mathematics, 308(7), 1222-1229 (2008)
Google Scholar

[ref8] Rautenbach Dieter and Sebastien Sereni Jean, Transversals of Longest Paths and Longest Cycles, CoRRabs, 1302-5503 (2013)
Google Scholar

[ref9] de Rezende Susanna F., Fernandes Cristina G., MartinDaniel M. and Wakabayashi Yoshika, IntersectingLongest Paths, Discrete Mathematics, 313, 1401-1408(2013)
Google Scholar

[ref10] Hippchen Thomas, , Intersections of Longest paths andLongest Cycles, Mathematical thesis, Georgia StateUniversity (2008)

[ref11] Attri Rajesh, Dev Nikhil and Sharma Vivek, Graphtheoretic approach(GTA)- A Multi Attribute DecisionMaking(MADM) Technique, Research Journal Engg, Science, 2(1), 50-53 (2013)
Google Scholar