A graph G is called claw-o-heavy if every induced claw (K1,3) of G has two end-vertices with degree sum at least ∣V(G)∣
Nearby in the stack
in
G
. For a given graph
R
,
G
is called
R
-f-heavy if for every induced subgraph
H
of
G
isomorphic to
R
and every pair of vertices
u,v∈V(H)
with
dH(u,v)=2
, there holds
max{d(u),d(v)}≥∣V(G)∣/2
. In this paper, we prove that every 2-connected claw-o-heavy and
Z3
-f-heavy graph is hamiltonian (with two exceptional graphs), where
Z3
is the graph obtained from identifying one end-vertex of
P4
(a path with 4 vertices) with one vertex of a triangle. This result gives a positive answer to a problem proposed in [B. Ning, S. Zhang, Ore- and Fan-type heavy subgraphs for Hamiltonicity of 2-connected graphs, Discrete Math. 313 (2013) 1715--1725], and also implies two previous theorems of Faudree et al. and Chen et al., respectively.