# INDUCTIVE CLASSES OF GRAPHS Definitions and Bibliography

In the paper an overview and bibliography on inductive definitions of classes of graphs is given.
Math. Subj. Class (1985): 05 C 10

Dear Colleagues,

In december 1987, during the XXX semester in Banach Center in Warsaw, I promissed to prepare, on the basis of my lectures, an overview on inductive definitions of classes of graphs. In November 1988 the first version with the extended bibliography from the paper [Bat86] was ready in LaTeX.

Since some participants of the Colloquium on Combinatorics (TU Braunschweig, 15-16th November 1996) expressed their interest for this overview I transfered it into HTML and put it on the Web. The data for last eight years are missing.

I would appreciate very much your comments and any additional information on the subject.

Vladimir Batagelj

## Definitions

general
simple graphs
2-connected [Lov79]
3-connected [Tut61], [Tho80]
minimally 3-connected [Daw86]
4-connected [Fon78]
2-edge connected [Lov79]
planar connected [Mon70], [Lau81], [Bat86]
2-connected [Lau81]
3-connected [Tut61], [Lau81]
4-connected [Bar73], [Fon78]
triangulations plane all [Eb891], [Bru00], [StR34], [BoF67]
delta >= 4 [Bat84], [Ba87b]
delta >= 5 [Bat83]
even: deg mod 2 = 0 [Bat84], [Ba87b]
projective plane [Bar82]
torus [Lav87]
cubic graphs all [Ba81b]
connected [Joh66], [Ore67], [Ba81b]
2-connected [Ba81b]
3-connected [Ba81b]
cyclically 4-edge connected [Fon78]
chi' = 3 [FJR78], [FJR81]
chi' = chi = 3 [FJR78], [FJR81]
bipartite [Bat94]
bipartite w.o. C4 [Ma887], [Bat94]
planar all [Ba81b]
connected [Ba81b]
connected bipartite [Ba81b]
3-connected all [ErM79]
bipartite [Bat84], [HMM85], [Ba87b]
w.o. C3 [Bat84], [Ba87b]
w.o. C3 and C4 [Bat83]
cyclically 4-connected [Kot68]
strongly cyclically 4-connected [Bar74]
cyclically 5-connected [Bar74], [But74]
strongly cyclically 5-connected [Bar77]
quadrangulations
of the plane
all [Ba87a]
3-connected [Ba87a]
4-regular graphs connected [Toi74], [BJF83]
planar connected [Man79], [Leh81]
3-connected [Ba87a]
r-regular (multi)graphs [Ba87c]
Eulerian graphs all [Bat96]
simple [Bat96]
simple planar [Bat96]

## Bibliography

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7. Batagelj V.: Inductive classes of cubic graphs. Colloquia Mathematica Societatis Janos Bolyai, 37. Finite and infinite sets, Eger 1981, 89-101.
8. Batagelj, V.: An inductive definition of the class of all triangulations with no vertex of degree smaller than 5. Proceedings of the Fourth Yugoslav Seminar on Graph Theory, Novi Sad 1983, 15-25.
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(presented at the First Malta Conference on Graphs and Combinatorics, 28. may - 2. june 1990).
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Vladimir Batagelj, Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
First version: November 21, 1985; First HTML version: November 21, 1996