. Bonomo, . Figueiredo, and G. Durán, Safe, and Szwarcfiter Ptolemaic graphs. Indeed, the corollary below shows that probe block graphs are a subclass of Ptolemaic graphs, and they are exactly those probe diamond-free graph that are chordal

]. D. Bayer, V. B. Le, and H. N. De-ridder, Probe threshold and probe trivially perfect graphs, Theoretical Computer Science, vol.410, issue.47-49, pp.47-494812, 2009.
DOI : 10.1016/j.tcs.2009.06.029

URL : http://doi.org/10.1016/j.tcs.2009.06.029

A. Berry, M. C. Golumbic, and M. Lipshteyn, Recognizing Chordal Probe Graphs and Cycle-Bicolorable Graphs, SIAM Journal on Discrete Mathematics, vol.21, issue.3, pp.573-591, 2007.
DOI : 10.1137/050637091

D. E. Brown and L. J. Langley, Probe interval orders The Mathematics of Preference Choice and Order, Essays in Honor of P. C. Fishburn, pp.313-322, 2009.

D. B. Chandler, M. Chang, T. Kloks, J. Liu, and S. Peng, Recognition of Probe Cographs and Partitioned Probe Distance Hereditary Graphs, Proceedings of the Second International Conference on Algorithmic Aspects in Information and Management, pp.267-278, 2006.
DOI : 10.1007/11775096_25

M. Chang, L. Hung, T. Kloks, and S. Peng, Block-graph width, Theoretical Computer Science, issue.23, pp.4122496-2502, 2011.
DOI : 10.1016/j.tcs.2010.10.041

URL : http://doi.org/10.1016/j.tcs.2010.10.041

M. Chang, L. Hung, and P. Rossmanith, Recognition of probe distance-hereditary graphs, Discrete Applied Mathematics, vol.161, issue.3, pp.336-348, 2013.
DOI : 10.1016/j.dam.2012.08.029

J. L. Chang, A. J. Kloks, and S. Peng, The PIGs Full Monty ??? A Floor Show of Minimal Separators, Lecture Notes in Computer Science, vol.3404, pp.521-532, 2005.
DOI : 10.1007/978-3-540-31856-9_43

M. C. Golumbic, Algorithmic graph theory and perfect graphs, Annals of Discrete Mathematics, vol.57, 2004.

M. C. Golumbic and M. Lipshteyn, Chordal probe graphs, Discrete Applied Mathematics, vol.143, issue.1-3, pp.221-237, 2004.
DOI : 10.1016/j.dam.2003.12.009

URL : https://hal.archives-ouvertes.fr/hal-00678308

M. C. Golumbic, F. Maffray, and G. Morel, A characterization of chain probe graphs, Annals of Operations Research, vol.55, issue.1, pp.175-183, 2011.
DOI : 10.1007/s10479-009-0584-6

URL : https://hal.archives-ouvertes.fr/hal-00660315

L. N. Grippo, Structural characterizations of intersection graphs, 2011.

P. Hell and J. Huang, Interval bigraphs and circular arc graphs, Journal of Graph Theory, vol.178, issue.4, pp.313-327, 2004.
DOI : 10.1002/jgt.20006

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.7538

J. L. Johnson and J. P. Spinrad, A polynomial time recognition algorithm for probe interval graphs, Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, 2001.

D. C. Kay and G. Chartrand, A characterization of certain ptolemaic graphs, Journal canadien de math??matiques, vol.17, issue.0, pp.342-346, 1965.
DOI : 10.4153/CJM-1965-034-0

V. Le and S. Peng, Characterizing and recognizing probe block graphs, Proceedings of the Workshop on Algorithms, Bioinformatics, and Computation Theory of the International Computer Symposium, ICS 2012 of Smart Innovation, Systems and Technologies, pp.7-13, 2012.
DOI : 10.1007/978-3-642-35452-6_2

R. M. Mcconnell and J. Spinrad, Construction of probe interval models, Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.866-875, 2002.

J. Spinrad, Circular-arc graphs with clique cover number two, Journal of Combinatorial Theory, Series B, vol.44, issue.3, pp.300-306, 1988.
DOI : 10.1016/0095-8956(88)90038-X

URL : http://doi.org/10.1016/0095-8956(88)90038-x

D. B. West, Introduction to graph theory, 1996.

P. Zhang, E. Schon, S. Fischer, E. C. , J. Weiss et al., An algorithm based on graph theory for ghe assembly of contigs in physical mapping of DNA, Computer Applications in the Biosciences, vol.10, issue.3, pp.309-317, 1994.