References in periodicals archive

(ii) A Eulerian graph is a graph whose all vertices have even degree.

Edge-partitioning graphs into regular and locally irregular components

Note that if a signed Eulerian graph contains an odd number of negative edges, it must contain an unbalanced cycle.

- [x.sub.n-1] - [x.sub.0] denote a signed Eulerian graph formed by the union of ([x.sub.i], [x.sub.i+1])-paths where i [member of] [Z.sub.n].

(i) [v.sub.a] - [v.sub.b] - w - [v.sub.a], which is the symmetric difference of [C.sub.b] and C', is an unbalanced Eulerian graph, so it contains an unbalanced cycle.

(ii) [v.sub.c] - [v.sub.d] - w - [v.sub.c], which is the symmetric difference of [C.sub.l] and C', is an unbalanced Eulerian graph, so it contains an unbalanced cycle.

(ii) [v.sub.a] - [v.sub.b] - [v.sub.c] - [v.sub.d] - w - [v.sub.a], which is the symmetric difference of Cl and the symmetric difference of C' and Cb, is an unbalanced Eulerian graph, so it contains an unbalanced cycle.

Then the symmetric difference of [C.sub.l] and C is an unbalanced Eulerian graph that contains an unbalanced cycle of length shorter than the length of the critical cycle [C.sub.l], a contradiction.

Homomorphisms of planar signed graphs to signed projective cubes

Polynomial-time algorithms are known for switching to a triangle-free graph [Hay96, HHW02], to a claw-free graph [JK08], to an eulerian graph [HHW02], to a bipartite graph [HHW02], and to a planar graph [EHHR00a, Kra03].

Parameterized problems related to Seidel's switching

To these we wish to add some 4-restrictions, which we should do in such a way as to produce an Eulerian graph at length 4.

Universal cycles for permutation classes

A characterization of Eulerian graphs with trianglefree Euler tours.

The complexity of [P.sub.4]-decomposition of regular graphs and multigraphs