"Dualizing distance-hereditary graphs,"
Discussiones Mathematicae Graph Theory to appear.
"Dual-chordal and strongly dual-chordal graphs,"
Journal of Combinatorial Mathematics and Combinatorial Computing 93 (2015) 53-63.
"When fundamental cycles span cliques,"
Congressus Numerantium 191 (2009) 213-218.
This paper
explores a duality between the maximal cliques and the unit disks
of a graph.
"S-minimal unions of disjoint cycles
and more odd eulerian characterizations,"
Congressus Numerantium 177 (2005) 129-132.
"Dualizing chordal graphs,"
Discrete Mathematics 263 (2003) 207-219.
"Recognizing dual-chordal
graphs," Congressus Numerantium 150 (2001) 97-103.
"Graph-theoretic model
of geographic duality," Annals of the New York Academy of
Sciences 555 (1989) 310-315.
A graph-theoretical
look at the dual tree structures of watercourses (streams) and
watersheds (divides), including the isthmus/strait duality and
a self-dual, Euleresque role of bridges.
"A clique/kernel analog
of eulerian," Congressus Numerantium 64
(1988) 171-178.
"Dualizing cubic graph
theory," Fundamenta Mathematicae 130
(1988) 67-72.
"Dual properties within
graph theory," Fundamenta Mathematicae 128
(1987) 91-97.
These
two papers emphasize the commonly overlooked fact that concepts
cannot be dualized; only particular formulations of the concepts
can be.
"A logical analogy
between directed and signed graphs," Utilitas Mathematica
32 (1987) 175-180.
"The logic of graph-theoretic
duality," American Mathematical Monthly 92
(1985) 457-464.
A more
accessible discussion of my "cycle-logical" approach to graph
duality, plus a rather unexpected duality between spanning trees
and edge cutsets.
"Balance and duality
in signed graphs," Congressus Numerantium 44
(1984) 11-18.
"Recharacterizing
eulerian: intimations of new duality," Discrete Mathematics
51 (1984) 237-242.
This is
where the characterization of a connected graph being eulerian
iff every edge is in an odd number of cycles (and being bipartite
iff every edge is in an odd number of cutsets) first appeared,
embedded in matroids and logic. You would probably prefer looking
at the following instead (or the Chartrand & Lesniak or Chartrand
& Oellermann textbooks):
H. Fleischner,
"Elementary proofs of (relatively) recent characterizations
of Eulerian graphs," Discrete Applied Mathematics
24 (1989) 115-119.
D. R. Woodall,
"A proof of McKee's Eulerian-bipartite characterization,"
Discrete Mathematics 84 (1990)
217-220.
"Logical aspects of
combinatorial duality," Canadian Mathematical Bulletin
27 (1984) 251-242.
"Prime implicant quantifiers
for matroids, graphs, and switching networks," Utilitas
Mathematica 24 (1983) 155-163.
"Duality principles
for binary matroids and graphs," Discrete Mathematics
43 (1983) 215-222.
"A quantifier for
matroid duality," Discrete Mathematics 34
(1981) 315-318.
These
papers show how the traditional cycle/cutset duality of graph
theory corresponds to the duality of the universal and existential
quantifiers in logic.
"Logical and matroidal
duality in combinatorial linear programming," Congressus
Numerantium 29 (1980) 667-672.
"A self-dual language
for graph theory," Journal of Combinatorial Theory (B)
21 (1979) 60-66.