Note: The references are not ordered alphabetically!

 1800 P. Erdos Some combinatorial, geometric and set theoretic problems in measure theory in Kölzow, D.; Maharam-Stone, D. (eds.), Measure Theory Oberwolfach, Lecture Notes in Mathematics 1089 (1983) 1801 T. Calamoneri, B. Sinaimeri Relating threshold tolerance graphs to other graph classes In Proc. of the 15th Italian Conference on Theoretical Computer Science ICTCS (2014) Available here. 1802 P.A. Golovach, P. Heggernes, N. Lindzey, R.M. McConnell, V. Fernandes dos Santos, J.P. Sprinrad, J.L. Szwarcfiter On recognition of threshold tolerance graphs and their complements Discrete Appl. Math. 216 No. 171-180 (2017) doi 10.1016/j.dam.2015.01.034 1803 V. Dujmovic, A. Por, D.R. Wood Track layouts of graphs DMTCS 6 No.2 497-522 (2004) 1804 M.D. Safe Characterization and linear-time detection of minimal obstructions to concave-round graphs and the circular-ones property J. Graph. Th. 93 No.2 268-298 (2020) 1805 V. Lozin, V. Zamaraev The structure and the number of $P_7$-free bipartite graphs European J. Combin 65 142-153 (2017) doi 10.1016/j.ejc.2017.05.008 1806 M. Jiang Recognizing d-interval graphs and d-track interval graphs Algorithmica 66 541-563 (2012) doi 10.1007/s00453-012-9651-5 1807 B.M.P. Jansen, V. Raman, M. Vatshelle Parameter ecology for feedback vertex set Tsinghua science and technology 19 No.4 387-409 (2014) 1808 Let us consider a $(C,S,I)$-partition of a pseudo-split graph $G$. If $S$ is empty, then $G$ is a split graph and therefore it is polar. Otherwise, $S$ induces a 5-cycle $(v_0,v_1,v_2,v_3,v_4)$ and we have that $(C\cup\{v_0,v_2\}, I\cup\{v_1,v_3,v_4\})$ is a polar partition of G. Hence pseudo-split graphs are polar. It can easily be verified that the join of $K_1$ with a 5-cycle is not monopolar, but the disjoint union of a 5-cycle with an independent set is. Hence, if for a $(C,S,I)$-partition of a pseudo-split graph both $C$ and $S$ are non-emtpy, then $G$ is not monopolar. If $S$ is empty, then $G$ is split and therefore monopolar and if $C$ is empty, then $G$ is also monopolar, as stated. Thus $G$ is monopolar iff at least one of $C,S$ is empty, which can be decided from the degree sequence of $G$ in linear time. (Esteban Contreras) 1809 F. Maffray Fast recognition of doubled graphs Theoretical Comp.Sci. 516 96-100 (2014 doi 10.1016/j.tcs.2013.11.020 1810 A. Munaro On line graphs of subcubic triangle-free graphs Discrete Math. 340 No.6 1210-1226 (2017) doi 10.1016/j.disc.2017.01.006 1811 A. Munaro Bounded clique cover of some sparse graphs Discrete Math. 340 No.9 2208-2216 (2017) doi 10.1016/j.disc.2017.04.004 1812 Z. Deniz, E. Galby, A. Munaro, B. Ries On contact graphs of paths on a grid Proc. of Graph Drawing 2018, LNCS 11282 317-330 (2018) 1813 E. Gioan, Ch. Paul, M. Tedder5, D. Corneil Practical and Efficient Circle Graph Recognition Algoritmica 69 No.4 759-788 (2014) 1814 S. Chaplick Intersection graphs of non-crossing paths Proceedings of the International Workshop on Graph-Theoretic Concepts in Computer Science WG 2019, LNCS 11789 (2019) doi 10.1007/978-3-030-30786-8_24 Available on arXiv. 1815 R. Adhikary, K. Bose, S. Mukherjee, B. Roy Complexity of maximum cut on interval graphs Proc. of 37th International Symposium on Computation Geometry 7:1-7:11 (2021) 1816 O. Cagirici, P. Hlineny, B. Roy On colourability of polygon visibility graphs 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science 21:1-21:14 (2018) 1817 Let $k$ be the size of a maximum independent set in $G$. For every set $S$ in $V(G)$ with $k$ vertices, we can check in linear time whether $G[S]$ is independent and $G\S$ is $P_3$-free. This gives an $O(V(G)^k)$ algorithm to decide whether $G$ is monopolar. (P. Ochem) 1818 O. Aichholzer, W. Mulzer, P. Schnider, B. Vogtenhuber NP-Completeness of Max-Cut for Segment Intersection Graphs In: 34th European Workshop on Computational Geometry, Berlin, Germany, March 21–23, 2018 Available here. 1819 J.E. Williamson On Hamilton-connected graphs Ph.D.-Thesis, Western Michigan University 1973 1820 O. Ore Hamilton connected graphs Journal de Mathematiques Pures et Appliquees XLII 21-27 (1963) 1821 P. Seymour How the proof of the Strong Perfect Graph Conjecture was found 2006 Available here 1822 W. Kennedy, G. Lin, G. Yan Strictly chordal graphs are leaf powers J. of Discrete Algorithms 4 no.4 511-525 (2006) doi 10.1016/j.jda.2005.06.005 1823 M.C. Golumbic, U.N. Peled Block duplicate graphs and a hierarchy of chordal graphs Discrete Appl. Math. 124 No.1-3 67-71 (2002) doi 10.1016/S0166-218X(01)00330-4 1824 G. Oriolo, U. pietropaoli, G. Stauffer On the recognition of fuzzy circular interval graphs Discrete Math. 312 No.8 1426-1435 (2012) doi 10.1016/j.disc.2011.12.029 1825 W. Kennedy Strictly chordal graphs and phylogenetic roots M.Sc.Thesis, University of Alberta (2005) 1826 A. Rafiey Recognizing interval bigraphs by forbidden patterns J. Graph Theory (2022) doi 10.1002/jgt.22792 1827 A graph can contain arbitrarily many diamonds and therefore has unbounded distance to block (P. Ochem). 1828 A graph $G$ satisfies the condition of Prop. 1 in [1456] J. Kratochvil, A. Kubena On intersection representations of co-planar graphs Discrete Math. 178 No.1-3 251-255 (1998) with $\tilde{G}$ a star (P. Ochem). 1829 A graph with maximum independent set bounded by $k$ that is 3-colourable has at most $3k$ vertices. (P. Ochem) 1830 Book thickness of an is at most 5: 4 pages for the graph [1777] M. Yannakakis Embedding planar graph in four pages Journal of Computer and System Sciences 38 36-67 (1989) and an extra page for the apex vertex. (P. Ochem) 1831 R. Belmonte, P. van 't Hof, M. Kaminski, D. Paulusma, D.M. Thilikos Characterizing graphs of small carving-width Discrete Appl. Math 161 No.13-14 1888-1893 (2013) doi 10.1016/j.dam.2013.02.036 1832 M. Barbato, D. Bezzi Monopolar graphs: Complexity of computing classical graph parameters Discrete Appl. Math. 291 277-285 (2021) doi 10.1016/j.dam.2020.12.023 1833 M. Chudnovsky, A. Scott, P. Seymour, S. Spirki Detecting an odd hole J. ACM 67 No.1 1-12 (2020) doi 10.1145/3375720 1834 Z. Füredi, F. Lazebnik, A. Seress, V.A. Ustimenko, A.J. Woldar Graphs of prescribed girth and bi-degree J. Combin. Th. Series B 64 No.2 228-239 (1995) doi 10.1006/jctb.1995.1033 1835 L.E. Trotter Line perfect graphs Mathematical Programming 12 No.2 255-259 (1977) doi 10.1007/BF01593791 1836 I.E. Zverovich Perfect cochromatic graphs Rutcor Research Report 16-2000