… These graphs are a generalization of the well-known blossoms that play an analogous
role in the study of P 2 ${P}_{2}$ . These graphs also play a key role when we consider 2-factors. …

… The main result of this paper says that there is a polynomial algorithm for finding a
decomposition of any given 4-regular graph into two triangle-free 2-factors (or showing that�…

… that are trees and in the fourth part we consider preimage graphs that are triangle-free.
Finally, in the fifth and sixth part we translate the results back to the original domain of claw-free …

… that are trees and in the fourth part we consider preimage graphs that are triangle-free.
Finally, in the fifth and sixth part we translate the results back to the original domain of claw-free …

… Then we apply the polyhedral description of 2-factors [10] to this final graph. Finally, the union
of … 2 and the linear system sufficient to define the 2-factors of the final graph defines PF (G). …

… triangle-free 2-matching problems in nonbipartite graphs and the simple square-free 2-matching
and \(K_{t,t}\)-free t-matching problems in bipartite graphs… ], in a triangle-free 2-matching …

… graph is subcubic. Yet if instead of (simple) 2-factors, we look at the problem of uncapacitated
2-factors… there exists a polyhedral description for arbitrary graphs, given by Cornu�jols and …

… closed claw-free graphs with clique covering number θ. By Theorem A, every G ∈ Gθ is
the line graph of some (unique) triangle-free graph H. Let D1(H) be the set of all degree 1 …

… for the triangle-free 2-matching problem in subcubic graphs, which have no … triangle-free
2-matchings in G. Let PF(G) denote the convex hull of incidence vectors of triangle-free 2-factors …

… we can restrict ourselves to line graphs of triangle-free graphs. … result holds for general
graphs, not necessarily triangle-free graphs, although we will only use it for triangle-free graphs in …