The study of circular chromatic number Xc (G) of a graph G, which is a refinement of its
chromatic number, has been very active in the past decade. Many nice results are obtained …

The circular chromatic number χ c (G) of a graph G (also known as 'the star-chromatic
number'), is a natural generalization of the chromatic number of a graph. In this paper, we …

A signed graph is a graph together with an assignment of signs to the edges. A closed walk
in a signed graph is said to be positive (negative) if it has an even (odd) number of negative …

We show that a planar graph with girth at least 20t− 2 3 has circular chromatic number at
most 2+ 1 t, improving earlier results. This follows from a general result establishing …

The odd edge connectivity of a graph G, denoted by λo (G), is the size of a smallest odd
edge cut of the graph. Let S be any given surface and ϵ be a positive real number. We …

We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is
bipartite and planar, admits a homomorphism to the signed projective cube of dimension …

We are interested in colouring a graph G=(V, E) together with an integral weight or demand
vector x=(xv: v∈ V) in such a way that xv colours are assigned to each node v, adjacent …

In this paper, the concept of circular rr‐flow in a mono‐directed signed graph (G, σ) (G,σ) is
introduced. That is a pair (D, f) (D,f), where DD is an orientation on GG and f: E (G)→(− r, r) …

Abstract A graph G is 5/2-critical if G has no circular 5/2-coloring (or equivalently,
homomorphism to C 5), but every proper subgraph of G has one. We prove that every 5/2 …

We conjecture that every planar graph of odd-girth 2k+ 1 admits a homomorphism to the
Cayley graph C (Z22k+ 1, S2k+ 1), with S2k+ 1 being the set of (2k+ 1)-vectors with exactly …