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)
  • 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
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
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
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
1837 G. Burosch, J.-M. Laborde
Characterization of grid graphs
Discrete Math. 87 No.1 85-88 (1991)
doi 10.1016/0012-365X(91)90074-C
1838 M.R. Cerioli, L. Faria, T.O. Ferreira, C.A.J. Martinhon, F. Protti, B. Reed
Partition into cliques for cubic graphs: Planar case, complexity and approximation
Discrete Appl. Math. 156 No.12 2270-2278 (2008)
doi 10.1016/j.dam.2007.10.015
1839 A. Grzesik, T. Klimosova, M. Pilipczuk
Polynomial-time Algorithm for Maximum Weight Independent Set on P6-free Graphs
ACM Transactions on Algorithms 18 No.1 1-57 (2022)
doi 10.1145/3414473
1840 O. Al-saadi, J. Radcliffe
Asteroidal sets and dominating paths
In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. LNCS 14461
doi 10.1007/978-3-031-49611-0_15
1841 P. Bachmann, I. Rutter, P. Stumpf
On 3-coloring circle graphs
doi 10.48550/arXiv.2309.02258
Available on arXiv
1842 B.S. Panda
The forbidden subgraph characterization of directed vertex graphs
Discrete Math. 196 No.1-3 239-256 (1999)
doi 10.1016/S0012-365X(98)00127-7
1843 A. Brandstaedt, C. Hundt, F. Mancini, P. Wagner
Rooted directed path graphs are leaf powers
Discrete Math. 310 No.4 987-910
doi 10.1016/j.disc.2009.10.006
1844 For any linear layout of the vertices of a graph, an endpoint $x$ in the Layout and an integer $b$, there can be at most $(b-1)^2$ edges of length $b$ crossing x. Hence cutwidth <= bandwidth$^2$. (M. Renken)