{1}

BONDY J A, MURTY U S R. Graph Theory [M]. GTM244 Berlin: Springer,

2008.
{2}

BABAI L, FRANKL P. Linear Algebra Methods in Combinatorics [M]. To

Appear.
{3}

LIU Yanpei. Embeddability in Graphs(in Chinese) [M]. Beijing:

Science Press Beijing, 2010: 241-244.
{4}

THOMASSEN C. Totally odd $K$-4 subdisions in 4-chromatic graphs [R].

Math Report No.1998-04. Denmak: Technical Uni of Denmark, 1998.
{5}

REDEI L. Ein kombinatorischer Satz [J]. Acta Litterarum ac

Scientiarum Szeged, 1934(7): 39-43.
{6}

FORCADE R. Parity of paths and circuits in tournaments [J]. Discrete

Mathematics, 1973(6): 115-118.
{7}

SZELE T, Kombinatorische Untersuchungen uber den gerichteten

vollstandigen Graphen [J]. Mat Fiz Lapok, 1943(50): 223-256.
{8}

ADAM A. Bemerkungen zum graphentheoretischen Satze von I, Fidrich

[J]. Acta Math. Acad Sci Hungar, 1965(16): 9-11.
{9}

TUTTE W T. On Hamiltonian circuits [J]. J London Mathematical

Society, 1968(21): 98-101.
{10}

THOMASON A. Hamiltonian cycles and uniquely colourable graphs

[C]//Advances in Graph Theory: Annals of Discrete Mathematics 3.

Amsterdam: North-Holland, Amsterdam, 1978: 259-268.
{11}

KRAWCZYK A. A note on finding a second hamiltonian cycle in cubic

graphs[J]. Preprint, Dec 5, 1995.
{12}

BLOKHUIS A. Polynomials in Finite Geometrial and Combinorics, in

Surveys in Combinatorics [C]//Proc. $14^\mathrm{th}$ British

Combinatorial Conference, London Math. Soc. Lecture Notes Ser. 187.

Cambridge: Combridge University Press, 1993, 35-52.
{13}

THOMASSEN C. Whitney's 2-switching theorem, cycle space, and arc

mappings of directed graphs [J]. Journal of Combinotorial Theorry

Ser B, 1989(46): 257-291.
{14}

BONDY J A, LOVASZ L. Cycles through specified vertices of a graph

[J]. Combinatorica, 1981(1): 117-140.


{15}

TUTTE W T. How to draw a graph [J]. Proceedings of the London

Mathematical Society, 1963(13): 743-768.
{16}

REN Han, LIU Yanpei, MA Dengju, et al. Generating cycle space of

graph on surfaces with mall genera [J]. European J Combinatorics,

2004(25): 1087-1105.
{17}

REN Han, DENG Mo. Short cycles structures and an open problem by

Mohar and Thomassen [J]. Science in China Ser A, 2006, 49(2):

212-224.
{18}

HARTMAN I B A. Long cycles generate the cycle space of a graph [J].

European J Combinatorics, 1984(4): 237-246.
{19}

WHITNEY H. Congruent graphs and the connectivity of graphs [J].

American J Mathematics, 1932(45): 150-168.


{20}

GOLDERG M, MOON J W. Arc mappings and tournament isomorphisms [J]. J

London Mathematical Society, 1971(3): 373-384.
{21}

MCCUAIG W D, ROSENFELD M. Parity of edges containing specified edges

[C]//Cycles in Graphs: Annals of Discrete Mathematics 27. Amsterdam:

North-Holland, 1985: 419-431.
{22}

LOVASZ L. Problem 5 [J]. Periodica Mathematica Hungariaca, 1974(4):

82.
{23}

REN Han, DENG Mo. Minimum cycle bases for graphs on surfaces [J].

Discrete Math,  2007(307): 2654-2660.
{24}

REN Han, CAO Ni. Finding short cycles in embedded graphs [J]. Front

Math in China, 2010, 5(2): 319-327.
{25}

REN Han, CAO Ni. Finding more short cycles in weighted graphs [J].

Submitted.
{26}

ROBERTSON N, SEYMOUR P D. Graph minors XIII: The disjoint paths

problem [J]. J Combinatorial Theory Ser B, 1995, 63: 65-110.
{27}

SEYMOUR P D. Matroid minors [M]//Handbook of Combinatorics.

Amsterdam: North-Holland, 1985: 419-431.
{28}

WHITNEY H. Planar graphs [J]. Fund Math, 1933(21): 73-84.
{29}

LEFSHETZ S. Planar graphs and related topics [J]. Proc Nat Acta Sci,

1965, (54): 1763-1765
{30}

MACLANE S. A combinatorial condition for planar graphs [J]. Fund

Math, 1937, (28): 22-32.