The main theorem of this paper provides partial results on some major open problems in
graph theory, such as Tutteʼs 3-flow conjecture (from the 1970s) that every 4-edge …

In 1950s, Tutte introduced the theory of nowhere-zero flows as a tool to investigate the
coloring problem of maps, together with his most fascinating conjectures on nowhere-zero …

Let G be a 2-edge-connected simple graph on n≥ 13 vertices and A an (additive) abelian
group with| A|≥ 4. In this paper, we prove that if for every uv∉ E (G), max {d (u), d (v)}≥ n/4 …

Tutte's 3-flow conjecture states that every 4-edge-connected graph admits a nowhere-zero 3-
flow. In this paper, we characterize all graphs with independence number at most 4 that …

Let G be a 2-edge-connected simple graph on n vertices, let A denote an abelian group with
the identity element 0, and let D be an orientation of G. The boundary of a function f: E (G)→ …

Let A be an Abelian group, n≥ 3 be an integer, and ex (n, A) be the maximum integer such
that every n-vertex simple graph with at most ex (n, A) edges is not A-connected. In this …

Abstract Tutte's 3-flow conjecture (1970's) states that every 4-edge-connected graph admits
a nowhere-zero 3-flow. A graph G admits a nowhere-zero 3-flow if and only if G has an …

Let G be a 2-edge-connected simple graph on n≥ 3 vertices and A an abelian group with|
A|≥ 3. If a graph G∗ is obtained by repeatedly contracting nontrivial A-connected subgraphs …

Nowhere-Zero 3-Flows of Graphs with Independence Number Two Page 1 Graphs and
Combinatorics (2013) 29:1899–1907 DOI 10.1007/s00373-012-1238-z ORIGINAL PAPER …

Let G be a (simple) graph on n≥ 3 vertices and (d 1,…, dn) be the degree sequence of G
with d 1≤⋯≤ d n. The classical Chvátal's theorem states that if dm≥ m+ 1 or dn− m≥ n− m …